**If x + y = 8 and x – y = 2, find the value of 2x**^{2} + 2y^{2}.

^{2}+ 2y

^{2}.

**Answer :**

We know that

**2 (x ^{2} + y^{2}) = (x + y)^{2} + (x – y)^{2}**

It is given that

x + y = 8 and x – y = 2

Substituting the values

2x^{2} + 2y^{2} = 8^{2} + 2^{2}

By further calculation

= 64 + 4

= 68

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