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Question
If a, b, c and dare in continued proportion, then prove that
ad (c2 + d2) = c3 (b + d)
Solution
ad (c2 + d2) = c3 (b + d)
`"a"/"b" = "b"/"c" = "c"/"d" = "k"`
⇒ c = kd
b =kc= k2d
a=kb=k3d
ac( c2 + d2 ) = c3(b + d)
LHS
ac( c2 + d2)
= k3d x c(k2 d2 + d2)
= k3d3 (k2d + d)
RHS
c3(b + d)
= k3d3(k2d + d)
LHS = RHS. Hence , proved.
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