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Question

a2+b2isequalto?


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Solution

To solve this we use some identities in some steps :

Step 1: Here we use (a+b)2=a2+b2+2ab

a2+b2=(a+b)2-2ab(after shifting the sides)

Step 2: Now we use the identity (a-b)2=a2+b2-2ab

a2+b2=(a-b)2+2ab

Step 3: Now we add the equation obtained in these two steps

a2+b2+a2+b2=(a+b)2-2ab+(a-b)2+2ab2a2+2b2=(a+b)2+(a-b)22(a2+b2)=(a+b)2+(a-b)2(a2+b2)=(a+b)2+(a-b)22

Hence, we get (a2+b2)=(a+b)2+(a-b)22.


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