#### Question

If a, b, c and dare in continued proportion, then prove that

ad (c^{2} + d^{2}) = c^{3} (b + d)

#### Solution

ad (c^{2} + d^{2}) = c^{3} (b + d)

`"a"/"b" = "b"/"c" = "c"/"d" = "k"`

⇒ c = kd

b =kc= k^{2}d

a=kb=k^{3}d

ac( c^{2} + d^{2} ) = c^{3}(b + d)

LHS

ac( c^{2} + d^{2})

= k^{3}d x c(k^{2} d^{2} + d^{2})

= k^{3}d^{3 }(k^{2}d + d)

RHS

c^{3}(b + d)

= k^{3}d^{3}(k^{2}d + d)

LHS = RHS. Hence , proved.

Is there an error in this question or solution?

Solution If A, B, C and Dare in Continued Proportion, Then Prove that Concept: Proportions.