Question

If (x − y)² = 152 and xy = 16, find the value of x² + y²

Answer 1

Given :

• (x - y)² = 152
• xy = 16

To Find :

• The value of  x² + y²

Solution :

Let,

(x - y)² = 152 ------------(1)

xy = 16 ------------(2)

Taking eq(1),

⇒ (x - y)² = 152

• by using algebric equation [(a - b)² = a² + b² - 2ab]

⇒ x² + y² - 2xy  = 152

⇒ x² + y² = 152 + 2xy

• From eq (2), [xy = 16]

⇒ x² + y² = 152 + 2 × xy

⇒ x² + y² = 152 + 2 × 16            

⇒ x² + y² = 152 + 32

⇒ x² + y² = 184

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

Given :

(x − y)² = 152 and xy = 16

To Find :

find the value of x² + y²

______________________________________________

Identity used here :

$\bold{\boxed{\boxed{\pink{ {(x- y)}^{2} = {x}^{2} + {y}^{2} - 2xy}}}}$

The Question is also in the form of (x − y)²

so we expand it :

$= > {(x - y)}^{2} = 152$

$= > {x}^{2} + {y}^{2} - 2xy = 152......(1)$

$= > xy = 16.....(2)$

From equation 2 we get xy=16 now put into equation 1.

$= > {x}^{2} + {y}^{2} - 2 \times 16 = 152$

$= > {x}^{2} + {y}^{2} - 32 = 152$

$= > {x}^{2} + {y}^{2} = 152 + 32 = 184$

$\bold{\boxed{\blue{∴ {x}^{2} + {y}^{2} = 184}}}$