Question

If (x, 2x - 10, 2x - 1) is a Pythagorean triple, what is the value of x?

Answer 1

Explanation:

According to the Pythagorean Theorem: a^2 + b^2 = c^2.

Here we assume that a = x, b = 2x -10 and c= 2x -1.

Then the following must be true:

x^2 + (2x - 10)^2 = (2x - 1)^2, or

x^2 + 4x^2 - 40x + 100 = 4x^2 - 4x + 1

This simplifies to

x^2 - 40x + 4x - 1 = 0, or

x^2 - 39x -1 = 0

In this quadratic, the coefficients are a = 1, b = -39 and c = -1.

The discriminant is thus b^2 - 4ac => (-39)^2 - 4(1)(-1), or 1521 + 4, or

1525. This positive discriminant tells us that there are two real, different roots. Here they are:

-(-39) ± √1525 39+39.05 -39.05+39

x = ---------------------- = ----------------- and x = -----------------

2 2 2

or x = 29.025 and x = -0.025