Question

If x2 + y2 = 14 and xy = 5, find the value of (1/2 x + 1/2 y)2.

Answer 1

Answer:

(½x+½y)²=6

Step-by-step explanation:

x^2 + y^2 = 14, xy=5

(A+B)^2=A^2 +2AB+B^2... (*)

(1/2x+1/2y)^2 =(*)

(1/2x)^2 +2(1/2x)(1/2y)+(1/2y)^2 =

1/4x^2 +1/2xy+1/4y^2=

1/4(x^2 +y^2) +1/2(xy)=

1/4*14+1/2*5=

14/4+5/2=

14/4+10/4=

24/4=6

let me know if I'm wrong.

Answer 2

( 1/2x +1/2y)²

= { ( x + y )/ 2xy }²

= ( x² + 2xy + y² )/4(xy)² —(1)

As we know that x² + y² = 14 — (2)

and xy = 5 —(3)

So, substitute the value of equation 2 and 3 in equation 1,

= ( x² + 2xy + y²)/4(xy)²

=( 14 + 2*5)/(4*5²)

= 24/(4*25)

= 6/25.