if a by b= c by d = e by f
(a2+c2+e2)(b2+d2+e2)=(ab+cd+
ef)
please tell the solution step by step
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Let a/b = c/d = e/f = k then
a = bk, c = dk and e = fk
L.H.S. = (ab + cd + ef)2
= (bk.b + dk.d + fk.f)2
= k2(b2 + d2 + f2)2
R.H.S. = (a2 + c2 + e2)(b2 + d2 + f2)
= (b2k2 + d2k2 + f2k2)(b2 + d2 + f2)
= k2(b2 + d2 + f2)(b2 + d2 + f2)
= k2(b2 + d2 + f2)2
L.H.S. = R.H.S.
Hence proved.
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