Question

If x-y=8 and xy=5, find x²+y² and x³+y³​

Answer 1

Step-by-step explanation:

The answer is -15

xy=12—equation 1

x+y=3—equation 2

To find: x²+ y²

We know that

(x+y)²=x²+y²+2xy —equation 3

We have in equation 1

=>x+y=3

Squaring both sides

=>(x+y)²=3²

=>(x+y)²=9

So the value of (x+y)² is 9

Secondly, we have in equation 2

=>xy=12

Multiplying 2 in both sides

=>2xy=2×12

=>2xy=24

So the value of 2xy is 24

Now we have the equation 3 that is (x+y)²=x²+y²+2xy, and by substituting the value of (x+y)² and 2xy in equation 3, we can get the value of x²+y²,

=>(x+y)²=x²+y²+2xy

=>9=x²+y²+24

=>9–24=x²+y²

=>x²+y²=-15

So the value of x²+y² is -15

pls folløw ❤️