Question

If a/b =b/c ,prove that [a+b+c] [a-b+c]=a²+b²+c² .

Answer 1

Answer:

Step-by-step explanation:

a/b = b/c

So a = b^2/c or ac = b^2

Given to prove that

(a+b+c)(a-b+c) = a^2 + b^2 + c^2

After opening the parentheses

a^2 - ab + ac + ab - b^2 + bc + ac - bc + c^2 = a^2 + b^2 + c^2

a^2 - b^2 + 2ac + c^2 = a^2 + b^2 + c^2

Now we showed that ac = b^2

So 2ac = 2b^2

a^2 -b^2+2b^2 + c^2 = a^2 + b^2 + c^2

So a^2 + b^2 + c^2 = a^2 + b^2 + c^2

Hence proved

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