Question

if a+b =10 and a^2+b^2=58 then fond a^3+b^3

Answer 1

a+b=10 and square on both sides, we get
${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab = 100$
=> it is given
${a}^{2} + {b}^{2} = 58$
2ab=100-58=42=> ab=21.
using the following formula
${x}^{3} + {y}^{3}= (x + y)( {x}^{2} + {y}^{2} - xy)$
we can evaluate
${a}^{3} + {b}^{3} = (a + b)( {a}^{2} + {b}^{2} - ab)$
=>
${a}^{3} + {b}^{3} = (10)(58 - 21) = 370.$
Hope it helps you...