If x + y = 10 and xy = 21, find 2 (x2 + y2).

If x + y = 10 and xy = 21, find 2 (x² + y²).

Answer :

We know that

(x + y)² = x² + y² + 2xy

It can be written as

x² + y² = (x + y)² – 2xy

It is given that

(x + y) = 10 and xy = 21

Substituting the values

x² + y² = 10² – 2 × 21

By further calculation

= 100 – 42

= 58

Here

2 (x² + y²) = 2 × 58 = 116

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