Question

if x + y = 8 and xy = 15/4, find the values of
(ii) 3(x2 + y2)
(iii) 5(x2 + y2) + 4(x - y).
(1) X-y​

Answer 1

Step-by-step explanation:

x+y = 8

xy = 15/4

Then,

(x+y)² = x²+y²+2xy

(8)² = x²+y²+2*15/4

64 = x²+y²+ 15/2

x²+y²= 64-15/2

x²+y²= 128-15/2

x²+y²= 113/2

1) (x-y) ² = x² + y² -2xy

= 113/2 - 2*15/4

= 113/2 -15/2

= 113-15/2

= 98/2

= 49

(x-y) = √49

= ±7

2) 3(x²+y²)

=3 ( 113/2)

= 339/2

=169.5

3) 5(x²+y²) + 4(x-y)

= 5(113/2) + 4(±7)

= 565/2 +4(±7)

= 282.5 + 4(±7)

if we take +7

= 282.5 + 4(7)

= 282.5 + 28

= 310.5

if we take -7

= 282.5 +4(-7)

= 282.5- 28

= 254.5

I hope it will help you..!!

Thank you..!!