**If x**^{2} + y^{2} = 34 and xy = 10 ½, find the value of 2 (x + y)^{2} + (x – y)^{2}.

^{2}+ y

^{2}= 34 and xy = 10 ½, find the value of 2 (x + y)

^{2}+ (x – y)

^{2}.

**Answer:**

It is given that

x^{2} + y^{2} = 34 and xy = 10 ½ = 21/2

We know that

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