[tex](x-y)^2=x^2-2xy+y^2=(x^2+y^2)-2(xy)\\\\\text{We have}\ (x-y)^2=100\ \text{and}\ xy=20.\\\\\text{Substitute}\\\\100=(x^2+y^2)-2(20)\\100=(x^2+y^2)-40\qquad\text{add 40 to both sides}\\\\140=(x^2+y^2)\\\\Answer:\ \boxed{x^2+y^2=140}[/tex]
Answer: The value of [tex]x^2+y^2[/tex] is 140
Step-by-step explanation:
We are given an expression:
[tex](x-y)^2=100[/tex]
And,
xy = 20
Using the identity:
[tex](a-b)^2=a^2+b^2-2ab[/tex]
Solving the expression:
[tex]x^2+y^2-2xy=100[/tex]
Putting the value of 'xy' in above equation, we get:
[tex]x^2+y^2-2(20)=100\\\\x^2+y^2=100+40\\\\x^2+y^2=140[/tex]
Hence, the value of [tex]x^2+y^2[/tex] is 140
