Question

If X+y= 8 and xy=15/4 - find - 5(x^2+y^2). + 4(x-y). What is the iden

Answer 1

Step-by-step explanation:

(x + y )² = (8)²

x²+2xy+y² = 64

x²+y² + 2 ( 15/4) = 64

x² + y² + 15/ 2 = 64

x²+ y² = 64 - ( 15/ 2 )

x²+ y² = 113/2 ..........(I)

Now, (x - y)² = x² - 2xy -y²

= x² + y² - 2 (xy)

= 113/2 - 15/2

= 49

therefore x - y = √ 49

x- y = 7 ...........(2)

Substituting value of 1 and 2

5( x² + y²) - 4 ( x- y )

5 (113/2) - 4 (7)

565/2 - 28

( 565 - 28) / 2

= 509 / 2