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AMC 10A 2021 Problem 9 | Factorizing Problem

Try this beautiful Problem based on Factorizing Problem from AMC 2021 Problem 9.

Factorizing Problem: AMC 10A 2021 Problem 9


What is the least possible value of $(x y-1)^{2}+(x+y)^{2}$ for real numbers $x$ and $y$ ?

  • 0
  • $\frac{1}{2}$
  • $\frac{1}{4}$
  • 1
  • 2

Key Concepts


Expansion of Polynomial

Factorization

Suggested Book | Source | Answer


AMC 10A 2021 Problem 9

1

Try with Hints


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 $x=y=0$. .

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Try this beautiful Problem based on Factorizing Problem from AMC 2021 Problem 9.

Factorizing Problem: AMC 10A 2021 Problem 9


What is the least possible value of $(x y-1)^{2}+(x+y)^{2}$ for real numbers $x$ and $y$ ?

  • 0
  • $\frac{1}{2}$
  • $\frac{1}{4}$
  • 1
  • 2

Key Concepts


Expansion of Polynomial

Factorization

Suggested Book | Source | Answer


AMC 10A 2021 Problem 9

1

Try with Hints


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 $x=y=0$. .

AMC-AIME Program at Cheenta

Subscribe to Cheenta at Youtube


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