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Maths-

General

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Question

$open vertical bar table row cell a to the power of 2 end exponent plus x to the power of 2 end exponent end cell cell a b end cell cell c a end cell row cell a b end cell cell b to the power of 2 end exponent plus x to the power of 2 end exponent end cell cell b c end cell row cell c a end cell cell b c end cell cell c to the power of 2 end exponent plus x to the power of 2 end exponent end cell end table close vertical bar$ is divisor of

$a^{2}$
$b^{2}$
$c^{2}$
$x^{2}$

The correct answer is: $x to the power of 2 end exponent$

$open vertical bar table row cell a to the power of 2 end exponent plus x to the power of 2 end exponent end cell cell a b end cell cell c a end cell row cell a b end cell cell b to the power of 2 end exponent plus x to the power of 2 end exponent end cell cell b c end cell row cell c a end cell cell b c end cell cell c to the power of 2 end exponent plus x to the power of 2 end exponent end cell end table close vertical bar$
Multiply $C subscript 1 end subscript comma C subscript 2 end subscript comma C subscript 3 end subscript$ by $a comma b comma c$ respectively and hence divide by abc
\ $capital delta equals fraction numerator 1 over denominator a b c end fraction open vertical bar table row cell a left parenthesis a to the power of 2 end exponent plus x to the power of 2 end exponent right parenthesis end cell cell a b to the power of 2 end exponent end cell cell c to the power of 2 end exponent a end cell row cell a to the power of 2 end exponent b end cell cell b left parenthesis b to the power of 2 end exponent plus x to the power of 2 end exponent right parenthesis end cell cell b c to the power of 2 end exponent end cell row cell c a to the power of 2 end exponent end cell cell b to the power of 2 end exponent c end cell cell c left parenthesis c to the power of 2 end exponent plus x to the power of 2 end exponent right parenthesis end cell end table close vertical bar$
Now take out a, b and c common from $R subscript 1 end subscript comma R subscript 2 end subscript$ and $R subscript 3 end subscript$ ,
\ $capital delta equals open vertical bar table row cell a to the power of 2 end exponent plus x to the power of 2 end exponent end cell cell b to the power of 2 end exponent end cell cell c to the power of 2 end exponent end cell row cell a to the power of 2 end exponent end cell cell b to the power of 2 end exponent plus x to the power of 2 end exponent end cell cell c to the power of 2 end exponent end cell row cell a to the power of 2 end exponent end cell cell b to the power of 2 end exponent end cell cell c to the power of 2 end exponent plus x to the power of 2 end exponent end cell end table close vertical bar$
Now applying $C subscript 1 end subscript rightwards arrow C subscript 1 end subscript plus C subscript 2 end subscript plus C subscript 3 end subscript$
$rightwards double arrow$ $capital delta equals left parenthesis a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent plus x to the power of 2 end exponent right parenthesis open vertical bar table row 1 cell b to the power of 2 end exponent end cell cell c to the power of 2 end exponent end cell row 1 cell b to the power of 2 end exponent plus x to the power of 2 end exponent end cell cell c to the power of 2 end exponent end cell row 1 cell b to the power of 2 end exponent end cell cell c to the power of 2 end exponent plus x to the power of 2 end exponent end cell end table close vertical bar$
Þ $capital delta equals x to the power of 4 end exponent left parenthesis a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent plus x to the power of 2 end exponent right parenthesis$
Hence, it is divisible by $x to the power of 2 end exponent$

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Physics-General

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parallel

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