Question

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Answer 1

Step-by-step explanation:

$\Large\mathtt{\fcolorbox{red}{pink}{\red{A N S W E R}}}$

To Prove :

( a + b + c )( a - b + c ) = a² + b² + c²

Proof :

a, b, c are in continued proportion

$•{} \frac{a}{b} = \frac{b}{c} : k \:(let \: it \: be) \\ b \: = ck \\ a = bk \\ (ck) = {ck}^{2} \\ •LHS = \\ ( {ck}^{2} + ck + c)(ck {}^{2} - ck + c) \\ = {c}^{2} ( {k}^{2} + k + 1)( {k}^{2} - k + 1) \\ = {c}^{2} \:[( {k}^{2} + 1) - ( {k}^{2}) ] \\ = {c}^{2} ( {k}^{4} + {2k}^{2} + 1 - {k}^{2} ) \\ = {c}^{2} ( {k}^{2} + {k}^{2} + 1) \\ \\• R.H.S = \\ {c}^{2} {k}^{4} + {c}^{2} {k}^{4} + {c}^{2} \\ = {c}^{2} ( {k}^{4} + {k}^{2} + 1)$

Hence LHS=RHS Proved

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