+1341 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).
+297 \(x+y=10 \)
\(x^3 + y^3 = 300 + x^2 + y^2\)
\(x^3+y^3=(x + y)(x^2 − xy + y^2)\)
\(10(x^2-xy+y^2)=300+x^2+y^2\)
\(9x^2-10xy+9y^2=300\)
\(9(x+y)^2-28xy=300\)
\(28xy=600\)
\(xy=\frac{150}{7}\)
\(x+y=10,xy=\frac{150}{7}\)
I think you can solve on your own now. If you are having trouble, leave a note and ill do the rest.
