Question

if x+y=9 and xy=20 then find the value of x²+y²

Answer 1

$x + y = 9 \\ (x+ y) {}^{2} = 9 {}^{2} \\ {x}^{2} + y ^{2} + 2xy = 81 \\ {x}^{2} + {y}^{2} = 81 - 2(20) \\ {x}^{2} + y {}^{2} = 41$

Answer 2

Answer:

41

Step-by-step explanation:

Given : x+y=9 and xy=20

To Find: the value of x²+y²

Solution:

Identity : $(x+y)^2=x^2+y^2+2xy$

We are given that  x+y=9 and xy=20

Substitute the values .

$(9)^2=x^2+y^2+2(20)$

$81=x^2+y^2+40$

$81-40=x^2+y^2$

$41=x^2+y^2$

Hence  the value of x²+y² is 41