If a, b, c are in continued proportion, then prove that b/ (b +c) = (a—b) / (a—c) by K-
method.
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Proof : a,b,c are in continued proportion.
∴ a/b = b/c =k (let)
b=ck
a=bk=(ck)k =ck ^2
L.H.S. =(ck ^2 +ck+c)(ck ^2 −ck+c)
=c ^2 (k ^2 +k+1)(k ^2 −k+1)
=c ^2 [(k ^2 +1) −(k) ^2 ]
=c ^2 [k ^4 +2k ^2 +1−k ^2 ]
=c ^2 [k ^4 +k 2 +1]
R.H.S. =c ^2 k ^4 +c ^2 k ^2 +c ^2
=c ^2 [k ^4 +k ^2+1]
L.H.S = R.H.S.
Step-by-step explanation:
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