Question

If p + q + r = 0, then
.p^2/qr+q^2/pr+r^2/pq
(1) 0
(3) 2
(2) 1
(4) 3​

Answer 1

Answer:

Ans is 3 (option 4)

Step-by-step explanation:

Given that, p + q + r = 0

Therefore,

$\frac{p^{2} }{qr}+\frac{q^{2} }{pr}+\frac{r^{2} }{pq}\\=\frac{p^{3}+q^{3}+r^{3}}{pqr}$ -------(i)

[We know that,

a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² -ab - bc - ca)

and if (a + b + c) =0, then a³ + b³ + c³ = 3abc]

Here (p + q + r) = 0, ∴ p³ + q³ + r³ = 3pqr

Now,

Putting the value of p³ + q³ + r³ = 3pqr in equation (i),

We get,

$\frac{3pqr}{pqr}\\ =3$

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