X-intercepts of (x²+y²-x)²=x²+y²

Question

how to find the x-intercepts?

Answer 1

The given equation is (x ^2 + y ^2 - x )^2 = x ^2 + y ^2.

To find x - intercept substitute y = 0 in given equation.

(x ^2 + 0^2 - x )^2 = x ^2 + 0^2

(x ^2 + 0 - x )^2 = x ^2 + 0

(x ^2 - x )^2 = x ^2

[x (x - 1)]^2 = x ^2

x ^2(x - 1)^2 = x ^2

(x - 1)^2 = 1

(x - 1)^2 = (± √1)^2

x - 1 = ± 1

x - 1 = 1 and x - 1 = - 1

x = 1 + 1 and x = 1 - 1.

x - intercepts are 0 and 2.