Question

If x+y=6, xy=13 , find x²+y²

Answer 1

$\huge\mathbb\fcolorbox{purple}{lavenderblush}{✰Answer}$

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

(x+y)^2 = 13+2*6 ( from given)

(x+y)^2 = 25

x+y = √25

x+y = 5 ———————————— Eqn 1

(x-y)^2 = x^2 + y^2–2xy

(x-y)^2 = 13–12 (from given)

x-y = √1

x-y = 1 —————————————Eqn 2

Add Eqn 1 and Eqn 2

we will get

2x = 6

x= 3

substitute x=3 in Eqn 1 or Eqn 2

we get y = 2

Answer :{x, y, x+y, x-y} = {3, 2, 5, 1}