Problem
ALG-B1-M06-P003 Sum and product
#3
★☆☆☆☆ Level 1 of 5
It is known that \(x+y=7\) and \(xy=10\). Find \(x^2+y^2\) and \(x^3+y^3\).
Express the powers through \(x+y\) and \(xy\).
\(x^2+y^2=(x+y)^2-2xy=49-20=29\).
Next, \(x^3+y^3=(x+y)^3-3xy(x+y)=343-210=133\).
There is no need to find \(x\) and \(y\) themselves.