Try this beautiful Problem based on Factorizing Problem from AMC 2021 Problem 9.
What is the least possible value of $(x y-1)^{2}+(x+y)^{2}$ for real numbers $x$ and $y$ ?
Expansion of Polynomial
Factorization
AMC 10A 2021 Problem 9
1
Expand the expression.
So, we get that the expression is $x^{2}+2 x y+y^{2}+x^{2} y^{2}-2 x y+1$ or $x^{2}+y^{2}+x^{2} y^{2}+1$.
Then the minimum value for this is 1 , which can be achieved at $x=y=0$. .
Try this beautiful Problem based on Factorizing Problem from AMC 2021 Problem 9.
What is the least possible value of $(x y-1)^{2}+(x+y)^{2}$ for real numbers $x$ and $y$ ?
Expansion of Polynomial
Factorization
AMC 10A 2021 Problem 9
1
Expand the expression.
So, we get that the expression is $x^{2}+2 x y+y^{2}+x^{2} y^{2}-2 x y+1$ or $x^{2}+y^{2}+x^{2} y^{2}+1$.
Then the minimum value for this is 1 , which can be achieved at $x=y=0$. .
