document.write( "Question 967458: if a/b = b/c prove that (a+b+c)(a-b+c) =(a^2 + b^2 + c^2) [ hints : let a/b = b/c = k therefore b = ck and a = ck^2] \n" ); document.write( "

Algebra.Com's Answer #594040 by anand429(138) $\"\"$ $\"About$

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Let $\"a%2Fb+=+b%2Fc+=+k\"$
\n" ); document.write( "therefore $\"b+=+ck\"$ and $\"a+=+ck%5E2\"$
\n" ); document.write( "So, LHS = $\"%28ck%5E2%2Bck%2Bc%29%2A%28ck%5E2-ck%2Bc%29\"$
\n" ); document.write( "= $\"c%2A%28k%5E2%2Bk%2B1%29%2Ac%2A%28k%5E2-k%2B1%29\"$
\n" ); document.write( "= $\"c%5E2%2A%28%28k%5E2%2B1%29%5E2-k%5E2%29\"$ (Using $\"%28x%2By%29%28x-y%29=x%5E2-y%5E2\"$ )
\n" ); document.write( "= $\"c%5E2%2A%28k%5E4%2B1%2B2k%5E2-k%5E2%29\"$
\n" ); document.write( "= $\"c%5E2%2A%28k%5E4%2Bk%5E2%2B1%29\"$
\n" ); document.write( "= $\"c%5E2%2Ak%5E4%2Bc%5E2%2Ak%5E2%2Bc%5E2\"$
\n" ); document.write( "= $\"%28ck%5E2%29%5E2+%2B+%28ck%29%5E2+%2B+c%5E2\"$
\n" ); document.write( "= $\"a%5E2%2Bb%5E2%2Bc%5E2\"$
\n" ); document.write( "= RHS. proved. \n" ); document.write( "

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