Question

If x-y =5 & xy = 15, then x²+y²=?

Answer 1

The value is,

`x^2 + y^2 = 55`

55

Explanation:

Now, we know that,

xy = 15, x-y = 5

using,

x - y = 5

squaring both sides and simplifying, we get,

`x-y=5\\(x-y)^2=5^2\\(x-y)^2=25\\x^2+y^2-2(xy)=25\\but\ we \ know\ that,\ xy = 15\\so,\\x^2+y^2-2(15)=25\\x^2+y^2-30=25\\x^2+y^2=25+30\\x^2+y^2=55`

Hence x^2 + y^2 = 55