Find the Pythagorean triple with the following equations: m=2, n=3... I'm thinking its a no solution?
To determine whether there is a Pythagorean triple with the given values of m=2 and n=3, we can use the formulas for generating Pythagorean triples.
The general formulas to generate Pythagorean triples are:
a = m^2 - n^2
b = 2mn
c = m^2 + n^2
Where a, b, and c represent the lengths of the sides of a right-angled triangle, with c representing the hypotenuse.
Let's plug in the values for m=2 and n=3 into these formulas:
a = 2^2 - 3^2 = 4 - 9 = -5
b = 2 * 2 * 3 = 12
c = 2^2 + 3^2 = 4 + 9 = 13
From these calculations, we can see that a is negative, which means that it cannot represent the length of a side in a right-angled triangle. Therefore, there is no solution for this particular combination of m=2 and n=3 to form a Pythagorean triple.
In summary, for m=2 and n=3, there is no Pythagorean triple.