Question

the value of x2 + y2 if x+y =7;xy =12 is----------------
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Answer 1

Solve the question as follows:

(x+y)²= x² + y² + 2xy

49= x²+y² +24

25= x²+y²

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Answer 2

Correct Question :-

Find the value of x² + y², if x + y = 7, xy = 12.

Answer :-

25

Solution :-

We know that

(x + y)² = x² + y² + 2xy

Here

• x + y = 7

• xy = 12

By substituting the values

⇒ (7)² = x² + y² + 2(12)

⇒ 49 = x² + y² + 24

Transpose 24 to LHS ( + 24 becomes - 24)

⇒ 49 - 24 = x² + y²

⇒ 25 = x² + y²

⇒ x² + y² = 25

Therefore the value of x² + y², if x + y =7; xy =12 is 25

Verification :-

(x + y)² = x² + y² + 2xy

⇒ (7)² = 25 + 2(12)

⇒ 49 = 25 + 24

⇒ 49 = 49

Identity used :-

• (x + y)² = x² + y² + 2xy