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The value of
Question

The value of

A.

1

B.

2

C.

0

D.

3

Correct option is A

Given: 
p2−(q−r)2(p+r)2−q2+q2−(p−r)2(p+q)2−r2+r2−(p−q)2(q+r)2−p2\frac{p^2 - (q - r)^2}{(p + r)^2 - q^2} + \frac{q^2 - (p - r)^2}{(p + q)^2 - r^2} + \frac{r^2 - (p - q)^2}{(q + r)^2 - p^2} 
Concept Used: 
We can find the value of the expression by letting the values of p, q and r.
Solution: 
Putting p = q = r = 1
p2−(q−r)2(p+r)2−q2+q2−(p−r)2(p+q)2−r2+r2−(p−q)2(q+r)2−p2\frac{p^2 - (q - r)^2}{(p + r)^2 - q^2} + \frac{q^2 - (p - r)^2}{(p + q)^2 - r^2} + \frac{r^2 - (p - q)^2}{(q + r)^2 - p^2}

12−(1−1)2(1+1)2−12+12−(1−1)2(1+1)2−12+12−(1−1)2(1+1)2−12\frac{1^2 - (1 - 1)^2}{(1 + 1)^2 - 1^2} + \frac{1^2 - (1 - 1)^2}{(1 + 1)^2 - 1^2} + \frac{1^2 - (1 - 1)^2}{(1 + 1)^2 - 1^2}
=13+13+13\frac{1}{3}+\frac{1}{3}+\frac{1}{3}
= 1
Thus, the value of the expression is 1. 

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