**If x + y = 10 and xy = 21, find 2 (x**^{2} + y^{2}).

^{2}+ y

^{2}).

**Answer :**

We know that

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

It can be written as

x^{2} + y^{2} = (x + y)^{2} – 2xy

It is given that

(x + y) = 10 and xy = 21

Substituting the values

x^{2} + y^{2} = 10^{2} – 2 × 21

By further calculation

= 100 – 42

= 58

Here

2 (x^{2} + y^{2}) = 2 × 58 = 116

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