SSC CGL 9 Aug 2015 Shift 1 Paper

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Question : 134 of 200

Marks: +1, -0

If

{m-a^2}/{b^2+c^2}

+

{m-b^2}/{c^2+a^2}

+

{m-c^2}/{a^2+b^2}

= 3 , then the value of m is

$a^2+b^2-c^2$
$a^2+b^2$
$a^2+b^2+ c^2$
$a^2-b^2-c^2$

Solution:

{m-a^2}/{b^2+c^2}

+

{m-b^2}/{c^2+a^2}

+

{m-c^2}/{a^2+b^2}

- 3 = 0
⇒

{m-a^2}/{b^2+c^2}

- 1 +

{m-b^2}/{c^2+a^2}

- 1 +

{m-c^2}/{a^2+b^2}

- 1 = 0
⇒

{m-a^2-b^2-c^2}/{b^2+c^2}

+

{m-b^2-c^2-a^2}/{c^2+a^2}

+

{m-x^2-a^2-b^2}/{a^2+b^2}

⇒

{m-(a^2+b^2+c^2)}/{b^2+c^2}

+

{m-(a^2+b^2+c^2)}/{c^2+a^2}

+

{m-(a^2++b^2+c^2)}/{a^2+b^2}

= 0
∴ Each term = 0
∴

{m-(a^2+b^2+c^2)}/{b^2+c^2}

= 0
⇒ m -

(a^2+b^2+c^2)

= 0
⇒ m =

a^2+b^2+c^2

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