Question

If a:b = c:d , then every ratio equals to a²+c²/b²+d²?
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Answer 1

Answer:

(i) Since a, b, c, d are in continued proportion then

a/b = b/c = c/d = k

⇒ a = bk, b = ck , c = dk

⇒ a = ck2

⇒ a = dk3, b = dk2 and c = dk

(ii) L.H.S. = (d2k6 + d2k4 + d2k2)(d2k4 + d2k2 + d2)

= d2k2 (k4 + k2 + 1).d2 (k4 + k2 + 1)

= d4k2(k4 + k2 + 1)2

R.H.S. = (ab + bc + cd)2

= (dk3.dk2 + dk2.dk + dk.d)2

= d4.k2(k4 + k2 + 1)2

L.H.S. = R.H.S.

Hence proved.