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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 $x=y=0$. .

AMC-AIME Program at Cheenta

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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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