Question

If a, b, c are in continued proportion and a(b-c) =2b, prove that : a-c=2(a+b)/a.

Answer 1

HELLO DEAR,

$suppose \: b = ax \: \: andc = bx \: where \: a \: \: and \: \: x \\ is \: not \: zero \: \\ then \: \: a(b - c) = 2means \\ a( ax - a {x}^{2} ) = 2ax \\ i.e \: \: \: (a - ax) = 2 \\ = > a(a - c) = a( {a} - ax^{2} ) = {a}^{2} (1 - {x}^{2} ) \\ = > {a}^{2} (1 - x)(1 + x) \\ = > a(1 - x) \times a(1 + x) \\ = > (a - ax)(a + ax) \\ = > a(a - c) = 2(a + b)$