Question

if x+y=3, x2+y2=5 then find the value of xy

Answer 1

x+y=3
x=3-y
putting the value of x
in this
x²+y²=5
(3-y) ²+y²=5
9-6y+y²+y²=5
2y²-6y+9-5=0
2y²-6y+4=0
2y²-4y-2y+4=0
2y(y-2)-2(y-2)=0
(2y-2) (y-2) =0
2y-2=0 or y-2=0
y=1 or y=2
so x=2 or 1
so x×y=2×1 or 1×2=2
I HOPE THIS WILL HELP YOU MARK ME BRAINLIEST

Answer 2

Given:

x+y=3, x^2+y^2=5

To Find:

find the value of xy

Solution:

It is given that x+y=3, x^2+y^2=5 and we need to find the value of xy, it can be found by squaring x+y=3,

The square of the above can be found by using the algebraic identity that is,

$(a+b)^2=a^2+b^2+2ab$

So using the identity to find the square, we have,

$(x+y)=3$

Squaring both sides we have,

[tex](x+y)^2=3^2\\ x^2+y^2+2xy=9[/tex]

Now substituting the value of x^2+y^2=5 in the equation,

[tex]x^2+y^2+2xy=9\\ 5+2xy=9\\ 2xy=4\\ xy=2[/tex]

Hence, the value of xy is 2.