Question

if (ap)^1/2+(bq)^1/2+(cr)^1/2={(a+b+c)(p+q+r)}^1/2 prove that a/p=b/q=c/r​

Answer 1

Answer:

Let. p/a + q/b + r/c =1. ……..(1)

a/p + b/q + c/r =0. ……. …. .(2)

Now squaring both sides of equation (1) , we get

[p/a + q/b + r/c]² = (1)²

=> (p/a)² + (q/b)² + (r/c)² + 2( pq/ab + qr/bc + pr/ac) = 1.

=> (p/a)² + (q/b)² +(r/c)² + 2[ pqr/abc ( c/r + a/p + b/q )] =1.

=> (p/a)² + (q/b)² + (r/c)² = 1. [ using equation (2)].

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