Find all ordered pairs x, y of real numbers such that x+y=10 and x^3 + y^3 = 300 + x^2 + y^2.

For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

kittykat Sep 8, 2024

#1**0 **

\(x+y=10 \)

\(x^3 + y^3 = 300 + x^2 + y^2\)

\(x^3+y^3=(x + y)(x^2 − xy + y^2)\)

\(10(x^2-xy+y^2)=300+x^2+y^2\)

\(9x^2-10xy+9y^2=300\)

\(9(x+y)^2-28xy=300\)

\(28xy=600\)

\(xy=\frac{150}{7}\)

\(x+y=10,xy=\frac{150}{7}\)

**I think you can solve on your own now. If you are having trouble, leave a note and ill do the rest.**

Imcool Sep 8, 2024