Question

if p, q and r are in continued proportion, prove that: p^2 + q^2 + r^2 = (p+q+r) (p-q+r) ​

Answer 1

If a,b,c are in continued proportion, then b

2

=ac or b=

ac

So, x=

p−q

p+q

×(p

2

−q

2

)

Formula

a

2

−b

2

=(a+b)(a−b)

Hence, x=

p−q

p+q

×((p+q)(p−q))

x=

(p+q)(p+q))

x=p+q