Find the coordinates of the intersection of the graphs of the function: y = √ x and y = x ^ 2

univerkov | September 23, 2021 | education

Substituting y = √x into the second equation, we get the equality:
√x = x ^ 2
we square this left and right sides of this equation, we get:

x = x ^ 4
x-x ^ 4 = 0
x * (1-x ^ 3) = 0
x1 = 0 1-x ^ 3 = 0
-x ^ 3 = -1
x2 = 1
Then :
y1 = √0 = 0 y2 = √1 = 1
We get two points of intersection: (0,0) and (1,1).

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