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Maths-

General

Easy

Question

If $a less or equal than fraction numerator s e c to the power of 2 end exponent invisible function application theta minus t a n invisible function application theta over denominator s e c to the power of 2 end exponent invisible function application theta plus t a n invisible function application theta end fraction less or equal than b$ then a+b=

$\frac{1}{3}$
$\frac{5}{3}$
$\frac{10}{3}$
$\frac{8}{3}$

The correct answer is: $fraction numerator 10 over denominator 3 end fraction$

$t a n invisible function application theta equals x$
$fraction numerator 1 minus x plus x to the power of 2 end exponent over denominator 1 plus x plus x to the power of 2 end exponent end fraction equals y$
$x to the power of 2 end exponent left parenthesis 1 minus y right parenthesis minus x left parenthesis 1 plus y right parenthesis plus left parenthesis 1 minus y right parenthesis equals 0$
$left parenthesis 1 plus y right parenthesis to the power of 2 end exponent minus 4 left parenthesis 1 minus y right parenthesis to the power of 2 end exponent greater or equal than 0$
$3 y to the power of 2 end exponent minus 10 y plus 3 less or equal than 0$
$y element of open square brackets fraction numerator 1 over denominator 3 end fraction comma 3 close square brackets$
$a equals fraction numerator 1 over denominator 3 end fraction comma b equals 3 semicolon a plus b equals fraction numerator 10 over denominator 3 end fraction$

Related Questions to study

The set of values of a for which the equation $blank x to the power of 3 end exponent minus 3 x plus a equals 0$ has three distinct real roots is

The set of values of a for which the equation $blank x to the power of 3 end exponent minus 3 x plus a equals 0$ has three distinct real roots is

Let $text end text alpha text end text$ and $text end text beta text end text$ be the roots of the equation $text end text x to the power of 2 end exponent minus p x plus r equals 0 text end text$ and $text end text fraction numerator alpha over denominator 2 end fraction text , end text blank 2 beta text end text$ be the roots of the equation $x to the power of 2 end exponent minus q x plus r equals 0 text . end text$ The value of $text end text text end text r text end text$ is

Let $text end text alpha text end text$ and $text end text beta text end text$ be the roots of the equation $text end text x to the power of 2 end exponent minus p x plus r equals 0 text end text$ and $text end text fraction numerator alpha over denominator 2 end fraction text , end text blank 2 beta text end text$ be the roots of the equation $x to the power of 2 end exponent minus q x plus r equals 0 text . end text$ The value of $text end text text end text r text end text$ is

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