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प्रश्न
If `a/c = c/d = c/f` prove that : `(a^3 + c^3)^2/(b^3 + d^3)^2 = e^6/f^6`
उत्तर
`a/c = c/d = c/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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