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If a b = b c , prove that ( a + b + c ) ( a − b + c ) = a 2 + b 2 + c 2

If a b = b c , prove that ( a + b + c ) ( a − b + c ) = a 2 + b 2 + c 2

Grade:9

1 Answers

Vikas TU
14149 Points
4 years ago
Dear Student,
: let a/b = b/c = k   
        a= ck^2 , b = ck , c=c
       (a+b+c)(a-b+c) = c^2( 1+k+k^2) ( k^2-k+1)
       = c^2 ( 1+k^2+k^4)
       = a^2+b^2+c^2
 Hnece proved.
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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