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Maths-

General

Easy

Question

If $a comma blank b blank$ and $blank c$ are the sides of a triangle, then the minimum value of $fraction numerator 2 a over denominator b plus c minus a end fraction plus fraction numerator 2 b over denominator c plus a minus b end fraction plus fraction numerator 2 c over denominator a plus b minus c end fraction$ is

3
9
6
1

The correct answer is: 6

$a plus b plus c equals 2 s comma$ then we have to find the minimum value of
$fraction numerator a over denominator s minus a end fraction plus fraction numerator b over denominator s minus b end fraction plus fraction numerator c over denominator s minus c end fraction equals negative 3 plus fraction numerator s over denominator s minus a end fraction plus fraction numerator s over denominator s minus b end fraction plus fraction numerator s over denominator s minus c end fraction$
Also, $fraction numerator fraction numerator s over denominator s minus a end fraction plus fraction numerator s over denominator s minus b end fraction plus fraction numerator s over denominator s minus c end fraction over denominator 3 end fraction greater or equal than fraction numerator 3 over denominator fraction numerator s minus a over denominator s end fraction plus fraction numerator s minus b over denominator s end fraction plus fraction numerator s minus c over denominator s end fraction end fraction blank open square brackets because A. M. greater or equal than H. M. close square brackets$
$because fraction numerator s minus a over denominator s end fraction plus fraction numerator s minus b over denominator s end fraction plus fraction numerator s minus c over denominator s end fraction equals 1 blank rightwards double arrow fraction numerator s over denominator s minus a end fraction plus fraction numerator s over denominator s minus b end fraction plus fraction numerator s over denominator s minus c end fraction greater or equal than 9$
Thus, the minimum value of the expression is 6

Related Questions to study

Let $alpha blank a n d blank beta$ be such that $pi less than alpha minus beta less than 3 pi.$ If $sin invisible function application alpha plus sin invisible function application beta equals negative fraction numerator 21 over denominator 65 end fraction blank a n d cos invisible function application alpha plus cos invisible function application beta equals negative fraction numerator 17 over denominator 65 end fraction comma$ then the value of $cos invisible function application fraction numerator alpha minus beta over denominator 2 end fraction$ is

Let $alpha blank a n d blank beta$ be such that $pi less than alpha minus beta less than 3 pi.$ If $sin invisible function application alpha plus sin invisible function application beta equals negative fraction numerator 21 over denominator 65 end fraction blank a n d cos invisible function application alpha plus cos invisible function application beta equals negative fraction numerator 17 over denominator 65 end fraction comma$ then the value of $cos invisible function application fraction numerator alpha minus beta over denominator 2 end fraction$ is

One of the general solutions of $4 sin to the power of 4 end exponent invisible function application x plus cos to the power of 4 end exponent invisible function application x equals 1$ is

One of the general solutions of $4 sin to the power of 4 end exponent invisible function application x plus cos to the power of 4 end exponent invisible function application x equals 1$ is

Which of the following is not the value of $sin invisible function application 27 degree minus cos invisible function application 27 degree ?$

Which of the following is not the value of $sin invisible function application 27 degree minus cos invisible function application 27 degree ?$

parallel

The sum of all roots of $sin invisible function application open parentheses pi log subscript 3 end subscript invisible function application open parentheses fraction numerator 1 over denominator x end fraction close parentheses close parentheses equals 0$ in $blank open parentheses 0 comma blank 2 pi close parentheses$ is

The sum of all roots of $sin invisible function application open parentheses pi log subscript 3 end subscript invisible function application open parentheses fraction numerator 1 over denominator x end fraction close parentheses close parentheses equals 0$ in $blank open parentheses 0 comma blank 2 pi close parentheses$ is

If $sin invisible function application theta subscript 1 end subscript plus sin invisible function application theta subscript 2 end subscript plus sin invisible function application theta subscript 3 end subscript equals 3 comma$ then $cos invisible function application theta subscript 1 end subscript plus cos invisible function application theta subscript 2 end subscript plus cos invisible function application theta subscript 3 end subscript$ is equal to

If $sin invisible function application theta subscript 1 end subscript plus sin invisible function application theta subscript 2 end subscript plus sin invisible function application theta subscript 3 end subscript equals 3 comma$ then $cos invisible function application theta subscript 1 end subscript plus cos invisible function application theta subscript 2 end subscript plus cos invisible function application theta subscript 3 end subscript$ is equal to

The set of values of $theta$ satisfying the inequation $2 sin to the power of 2 end exponent invisible function application theta minus 5 sin invisible function application theta plus 2 greater than 0$ , where $0 less than theta less than 2 pi$ , is

The set of values of $theta$ satisfying the inequation $2 sin to the power of 2 end exponent invisible function application theta minus 5 sin invisible function application theta plus 2 greater than 0$ , where $0 less than theta less than 2 pi$ , is

parallel

In any triangle $A B C comma fraction numerator a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent over denominator R to the power of 2 end exponent end fraction$ has the maximum value of

In any triangle $A B C comma fraction numerator a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent over denominator R to the power of 2 end exponent end fraction$ has the maximum value of

In triangle $A B C comma blank a equals 5 comma blank b equals 4 blank$ and $blank c equals 3. blank G$ is the centroid of the triangle. Circumradius of triangle $G A B$ is equal to

In triangle $A B C comma blank a equals 5 comma blank b equals 4 blank$ and $blank c equals 3. blank G$ is the centroid of the triangle. Circumradius of triangle $G A B$ is equal to

We are given $b comma blank c blank$ and $sin invisible function application B$ such that $B$ is acute and $b less than c sin invisible function application B.$ Then

We are given $b comma blank c blank$ and $sin invisible function application B$ such that $B$ is acute and $b less than c sin invisible function application B.$ Then

parallel

Number of ordered pair $open parentheses s close parentheses open parentheses a comma blank b close parentheses$ for each of which the equality $a open parentheses cos invisible function application x minus 1 close parentheses plus b to the power of 2 end exponent equals cos invisible function application open parentheses a x plus b to the power of 2 end exponent close parentheses minus 1$ holds true for all $x element of R$ are

Number of ordered pair $open parentheses s close parentheses open parentheses a comma blank b close parentheses$ for each of which the equality $a open parentheses cos invisible function application x minus 1 close parentheses plus b to the power of 2 end exponent equals cos invisible function application open parentheses a x plus b to the power of 2 end exponent close parentheses minus 1$ holds true for all $x element of R$ are

$I f tan invisible function application x equals b divided by a comma blank t h e n blank square root of open parentheses a plus b close parentheses divided by open parentheses a minus b close parentheses end root plus square root of open parentheses a minus b close parentheses divided by open parentheses a plus b close parentheses end root$ is equal to

$I f tan invisible function application x equals b divided by a comma blank t h e n blank square root of open parentheses a plus b close parentheses divided by open parentheses a minus b close parentheses end root plus square root of open parentheses a minus b close parentheses divided by open parentheses a plus b close parentheses end root$ is equal to

The total number of solution of $sin to the power of 4 end exponent invisible function application x plus cos to the power of 4 end exponent invisible function application x equals sin invisible function application x cos invisible function application x$ in $blank open square brackets 0 comma blank 2 pi close square brackets blank$ is equal to

The total number of solution of $sin to the power of 4 end exponent invisible function application x plus cos to the power of 4 end exponent invisible function application x equals sin invisible function application x cos invisible function application x$ in $blank open square brackets 0 comma blank 2 pi close square brackets blank$ is equal to

parallel

$I f cos to the power of 2 end exponent invisible function application A plus cos to the power of 2 end exponent invisible function application B plus cos to the power of 2 end exponent invisible function application C equals 1 comma blank t h e n blank increment A B C blank i s$

$I f cos to the power of 2 end exponent invisible function application A plus cos to the power of 2 end exponent invisible function application B plus cos to the power of 2 end exponent invisible function application C equals 1 comma blank t h e n blank increment A B C blank i s$

If $cos invisible function application p theta plus cos invisible function application q theta equals 0 comma blank$ then the different values of $theta$ are in A.P. where the common difference is

If $cos invisible function application p theta plus cos invisible function application q theta equals 0 comma blank$ then the different values of $theta$ are in A.P. where the common difference is

If $x subscript 1 end subscript blank a n d blank x subscript 2 end subscript$ are the roots of the equation $e to the power of 2 end exponent blank. x to the power of ln invisible function application x end exponent equals x to the power of 3 end exponent blank w i t h blank x subscript 1 end subscript greater than x subscript 2 end subscript comma$ then

If $x subscript 1 end subscript blank a n d blank x subscript 2 end subscript$ are the roots of the equation $e to the power of 2 end exponent blank. x to the power of ln invisible function application x end exponent equals x to the power of 3 end exponent blank w i t h blank x subscript 1 end subscript greater than x subscript 2 end subscript comma$ then

parallel

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