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Questions
If `a/c = c/d = e/f` prove that: `(a^3 + c^3)^2/(b^3 + d^3)^2 = e^6/f^6`
If `a/c = c/d = e/f` prove that (a3 + c3)2 : (b3 + d3)2 = e6 : f6
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Solution
`a/c = c/d = e/f` = k(say)
∴ a = bk, c = dk, e =fk
L.H.S.
= `(a^3 + c^3)^2/(b^3 + d^3)^2`
= `(b^3k^3 + d^3k^3)^2/(b^3 + d^3)^2`
= `[k^3(b^3 + d^3)]^2/(b^3 + a^3)^2`
= `(k^6(b^3 + d^3)^2)/(b^3 + d^3)^2`
= k6
R.H.S. = `e^6/f^6`
= `f^6k^6/f^6`
= k6
∴ L.H.S. = R.H.S.
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