Question

If x 2 + y 2 = 16 and xy = 7 then find the value of ( 1/2 x + 1/2 y ) 2

Answer 1

Step-by-step explanation:

x^2+y^2=16 xy=7

x^2 +y^2=(x+y)^2-2xy

=>16=(x+y)^2-2×7

=>16=(x+y)^2-14

=>(x+y)^2=30

=>x+y= root 30

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

=(x/2+y/2)2

=2{(x+y)/2}

=x+y

=root 30