SOLUTION: 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]

Algebra ->  Expressions-with-variables -> SOLUTION: 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]      Log On


   

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]
Answer by anand429(138) About Me  (Show Source):
You can put this solution on YOUR website!
Let a%2Fb+=+b%2Fc+=+k
therefore b+=+ck and a+=+ck%5E2
So, LHS = %28ck%5E2%2Bck%2Bc%29%2A%28ck%5E2-ck%2Bc%29
= c%2A%28k%5E2%2Bk%2B1%29%2Ac%2A%28k%5E2-k%2B1%29
= c%5E2%2A%28%28k%5E2%2B1%29%5E2-k%5E2%29 (Using %28x%2By%29%28x-y%29=x%5E2-y%5E2)
= c%5E2%2A%28k%5E4%2B1%2B2k%5E2-k%5E2%29
= c%5E2%2A%28k%5E4%2Bk%5E2%2B1%29
= c%5E2%2Ak%5E4%2Bc%5E2%2Ak%5E2%2Bc%5E2
= %28ck%5E2%29%5E2+%2B+%28ck%29%5E2+%2B+c%5E2
= a%5E2%2Bb%5E2%2Bc%5E2
= RHS. proved.