Algebra and Applications Test 1

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Question : 36 of 40

Marks: +1, -0

If

p + q + r = 0

and

pqr ≠ 0

, then what is the value of

1/{p^2+q^2-r^2}+1/{ q^2+r^2-p^2} +1/{ r^2+p^2-q^2}

0
1
-1
$1 /2$
None of these

Solution:

∵ p + q + r = 0

⇒ p + q =- r

⇒ (p + q)^2 = r^2

⇒ p^2 + q ^2+2pq = r^2

⇒ p^2 + q ^2- r^2 =-2pq

Similarly,

{ q^2+r^2-p^2}=-2pq

and

q^2 + r^2 - p^2 = -2rp

∴1/{p^2+q^2-r^2}+1/{ q^2+r^2-p^2} +1/{ r^2+p^2-q^2}

=-1/{2pq}-1/{2qr}-1/{2rp}

=-({p+q+r}/{2pqr})=0

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