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

Step-by-step 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

black/brown

step-by-step explanation:

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step-by-step explanation: