what value of x will make x,63,65 a pythagorean triple?
To determine the value of x that will make x, 63, and 65 a Pythagorean triple, we can use the Pythagorean theorem. According to the theorem, in a Pythagorean triple, if a, b, and c are positive integers, then:
a^2 + b^2 = c^2
In this case, x is the unknown value, and we are given that the triple is x, 63, and 65. Applying the Pythagorean theorem:
x^2 + 63^2 = 65^2
Simplifying the equation:
x^2 + 3969 = 4225
Subtracting 3969 from both sides:
x^2 = 256
Taking the square root of both sides:
x = ± 16
Therefore, the two values of x that will make x, 63, and 65 a Pythagorean triple are x = 16 and x = -16.