Question

if a/b=b/c=k . Then find values of (a+b+c)(a-b+c)=(a²+b²+c²)​

Answer 1

Step-by-step explanation:

$\frac{a}{b} = \frac{b}{c} = k$

=> b = ck

=> a = bk = ck. k = ck^2

L. H. S.,

(a + b + c) (a - b + c)

$= (c {k}^{2} + ck + c)(c {k}^{2} - ck + c)$

$= c( {k}^{2} + k + 1)c( {k}^{2} - k + 1)$

$= {c}^{2} ( {k}^{2} + k + 1)( {k}^{2} - k + 1)$

R. H. S.,

$( {a}^{2} + {b}^{2} + {c}^{2} )$

$= ( { {ck}^{2} )}^{2} + ( {ck)}^{2} + {c}^{2}$

$= {c}^{2} {k}^{4} + {c}^{2} {k}^{2} + {c}^{2}$

$= {c}^{2} ( {k}^{4} + {k}^{2} + 1)$

$= {c}^{2} ( {k}^{4} + 2 {k}^{2} + 1 - {k}^{2} )$

$= {c}^{2} (( { {k}^{2} + 1) }^{2} - ({k)}^{2} )$

$= {c}^{2} ( {k}^{2} + k + 1)( {k}^{2} - k + 1)$

therefore,

L. H.S = R. H. S