Question

if x - y =5 and xy=24, find the value of (x+y)

Answer 1

Answer :-

$\bf\huge\boxed{x + y = 11}$

Solution :-

x - y = 5

xy = 24

We know that,

(x + y)² = (x - y)² + 4xy

Putting the values

=> (x + y)² = (5)² + 4 × 24

=> (x + y)² = 25 + 96

=> (x + y)² = 121

=> (x + y) = √121

=> (x + y) = 11

Hence the value of (x + y) is 11 respectively.

Answer 2

Answer :-

The value of x + y is 11

Solution :-

We know that

(x + y)² = (x - y)² + 4xy

Here

• x - y = 5

• xy = 24

By substituting the values

⇒ (x + y)² = (5)² + 4(24)

⇒ (x + y)² = 25 + 96

⇒ (x + y)² = 121

⇒ x + y = √121

⇒ x + y = 121

Alternate way of solving

We know that

(x - y)² = x² + y² - 2xy

Here

• x - y = 5

• xy = 24

By substituting the values

⇒ (5)² = x² + y² - 2(24)

⇒ 25 = x² + y² - 48

⇒ 25 + 48 = x² + y²

⇒ x² + y² = 73

We know that

(x + y)² = x² + y² + 2xy

Here

• x² + y² = 73

• xy = 24

By substituting the values

⇒ (x + y)² = 73 + 2(24)

⇒ (x + y)² = 73 + 48

⇒ (x + y)² = 121

⇒ x + y = √121

⇒ x + y = 11

Therefore the value of x + y is 11.