Answer:
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
