Find the value of 2 (x + y)2 + (x – y)2.

If x² + y² = 34 and xy = 10 ½, find the value of 2 (x + y)² + (x – y)².

Answer:

It is given that

x² + y² = 34 and xy = 10 ½ = 21/2

We know that

(x + y)² = x² + y² + 2xy

Substituting the values

(x + y)² = 34 + 2 (21/2)

So we get

(x + y)² = 55 ….. (1)

We know that

(x – y)² = x² + y² – 2xy

Substituting the values

(x – y)² = 34 – 2 (21/2)

So we get

(x – y)² = 34 – 21 = 13 ….. (2)

Using both the equations

2 (x + y)² + (x – y)² = 2 × 55 + 13 = 123

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