Question

X-y=7 xy=9 find the value of x2+y2

Answer 1

(x-y) = 7
x2 + y2 - 2xy = 49
x2 + y2 - 18 = 49
x2 + y2 = 67

Answer 2

Correct Question :-

If x - y = 9 and xy = 9, then find the value of x² + y².

Answer :-

x² + y² = 67

Solution :-

We know that

(x - y)² = x² + y² - 2xy

Here

• x - y = 7

• xy = 9

By substituting the values

⇒ (7)² = x² + y² - 2(9)

⇒ 49 = x² + y² - 18

Transpose - 18 to LHS

⇒ 49 + 18 = x² + y²

⇒ 67 = x² + y²

⇒ x² + y² = 67

Therefore the value of x² + y² is 67.

Verification :-

(x - y)² = x² + y² - 2xy

⇒ (7)² = 67 - 2(9)

⇒ 49 = 67 - 18

⇒ 49 = 49

Identity used :-

• (x - y)² = x² + y² - 2xy