Hi!

Could you help me solve this problem?

Integers satisfying the equation

are vertexes of a certain polygon. What is its area?

Thank you.

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- Oct 12th 2011, 09:48 AMgollumPolynomial, area of a polygon
Hi!

Could you help me solve this problem?

Integers satisfying the equation

are vertexes of a certain polygon. What is its area?

Thank you. - Oct 12th 2011, 11:28 AMSorobanRe: Polynomial, area of a polygon
Hello, gollum!

I used some Olympic-level gymnastics . . .

Quote:

Integers satisfying the equation:

are vertexes of a certain polygon. .What is its area?

We have a quadratic in

Quadratic Formula: .

. .

Since is an integer, the radicand must be a square.

. . . . . .

Hence, we have: .

The difference of two squares is 20.

. . The only such squares are: .

This gives us: .

. . . . . . and: .

We have four vertices:

. .

We have a parallelogram with base 4 and height 5 . . .