Question

Which combination of integers can be used to generate the Pythagoreantriple (7.24,25)?A. x = 1, y = 3B. X = 3.y = 2C. X = 2.y = 2D. * = 4y = 3SUB

Answer 1

It is important to know that a Pythagorean Triple is a set of three numbers that satisfy the Pythagorean Theorem

`c^2=a^2+b^2`

Then, we form the following equations

`\begin{gathered} a=x^2-y^2 \\ b=2xy \\ c=x^2+y^2 \end{gathered}`

These equations are deducted from the Pythagorean Theorem. The correct numbers must satisfy these equations for a = 7, b = 24, and c = 25.

Now, we just evaluate each answer choice to see which one meets these equations.

Option A is not correct because x must be greater than y, otherwise, the solution won't be real.

Option B.

`a=3^2-2^2=9-4=5`

Option B is not correct because doesn't meet the first expression.

Option D.

`\begin{gathered} a=4^2-3^2=16-9=7 \\ b=2\cdot4\cdot3=24 \\ c=4^2+3^2=16+9=25 \end{gathered}`

Hence, D is the correct answer.