b-x-y-c-are-consecutive-terms-of-a-G-P-x-br-y-br-2-c-br-3-A-M-between-b-and-c-is-a-b-c-2-a-2a-b-c-2abc-

Question Number 118298 by hmh2k20 last updated on 16/Oct/20

b, x, y, c are consecutive terms of a G . P .

∴ x = br, y = {br}^{2}, c = {br}^{3}

A . M . between b and c is a

∴ \frac{b + c}{2} = a \Rightarrow 2 a = b + c

2 a bc = (b + c) bc

= b^{2} c + b c^{2}

= b^{2} ({br}^{3}) + b {({br}^{3})}^{2}

= b^{3} r^{3} + b^{3} r^{6}

= {(br)}^{3} + {({br}^{2})}^{3}

= x^{3} + y^{3}

∴ x^{3} + y^{3} = 2 abc \leftarrow

Commented by prakash jain last updated on 16/Oct/20

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