CPM Homework Help : A2C Problem 9-159

Verify that the graphs of the equations $x^{2} + y^{3} = 17$ and $x^{4} − 4y^{2} − 8xy = 17$ intersect at $\left(3, 2\right)$ .

Step 1:

Insert the values of the point into the equations.

$3^{2} + 2^{3} = 17\\3^{4} − 4\left(2^{2}\right) − 8\left(3\right)\left(2\right) = 17$

Step 2:

Simplify.

$9 + 8 = 17$

$81 − 16 − 48 = 17$

Answer:

$17 = 17\\17 = 17$