a) Cho \(x + y = 15\) và \(xy = 56\). Tính \({x^2} + {y^2}\).
b) Cho \(a + b = 10\) và \(ab = 21\) . Tính \({a^3} + {b^3}\).
\(\eqalign{ & a)\,\,{x^2} + {y^2} = {x^2} + {y^2} + 2xy – 2xy \cr & \,\,\,\,\, = \left( {{x^2} + 2xy + {y^2}} \right) – 2xy = {\left( {x + y} \right)^2} – 2xy \cr & \,\,\,\,\, = {15^2} – 2.56 = 113 \cr & b)\,\,{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} – ab + {b^2}} \right) \cr & \,\,\,\,\, = \left( {a + b} \right)\left[ {\left( {{a^2} + {b^2}} \right) – ab} \right] \cr & \,\,\,\,\, = \left( {a + b} \right)\left[ {{{\left( {a + b} \right)}^2} – 2ab – ab} \right] \cr & \,\,\,\,\, = \left( {a + b} \right)\left[ {{{\left( {a + b} \right)}^2} – 3ab} \right] \cr & \,\,\,\,\, = 10\left( {{{10}^2} – 3.21} \right) = 370 \cr} \)