Question

How to solve this problem?
\(\large \begin{cases} { x }^{ 3 }-{ y }^{ 3 }+(3{ x }^{ 2 }-y+2)\sqrt { y+1 } -(3{ y }^{ 3 }-x+2)\sqrt { x+1 } =0 \\ { x }^{ 2 }+{ y }^{ 2 }-7x-6y+14=0 \end{cases} \)

Answer 1

Note that the 1st curve is symmetrical about x=y line.
On substituting y=x in that eqn, you find its a solution !
Now we are left with x=y and x^2 + y^2 - 7x - 6y + 14 = 0
See if they have a solution in common.

Answer 2

yup :) thank you