If x+y=3 and xy=2 find the value of x^2+y^2

Question

asked Mar 7, 2022 27.4k views

2 Answers

Theduck · Answer 1 · 2022-03-10T16:42:02+0000

Answer:

5

Explanation:

We know that

x + y = 3

and

xy = 2

Solve for x in first variable

x = 3 - y

Substitute this into second equation

(3 - y)y = 2

$- {y}^(2) + 3y - 2$

Simplify

${y}^(2) - 3y + 2$

(y - 1)(y - 2)

y = 1

y = 2

So x or y can be

$x = 1 \: \: y = 2$

or

$x = 2 \: \: \: y = 1$

So we need to find x^2 and y^2.

${2}^(2) + {1}^(2) = 5$