Question

if x?+y?=89 and xy=40 then find the value of x?+y?:

Q. x²+y²=89 and xy =40 then find the value of x³+y³.

Answer 1

Dear Student,
$$\begin{gathered} Given: \\ {x}^2+y^2=89 \\ xy=40 \\ {\left(x+y\right)}^2=x^2+y^2+2xy \\ {\left(x+y\right)}^2=89+2\times 40 \\ =89+80 \\ =169 \\ \left(x+y\right)=\sqrt{169} \\ \left(x+y\right)=13 \\ Now, \\ {x}^3+y^3=\left(x+y\right)\left(x^2+y^2-xy\right)\left[a^3+b^3=(a+b)(a^2-ab+b^2)\right] \\ =13\left(89-40\right) \\ =13\times 49 \\ =\mathbf{637} \end{gathered}$$
Regards