Question

if a+b=10,a^2+b^2=50,find a^3+b^3​

Answer 1

Step-by-step explanation:

Given: a + b = 10,

${a}^{2} + {b}^{2} = 50 \\ \\ \because {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ \therefore \: ( {10)}^{2} = 50 + 2ab \\ 100 - 50 = 2ab \\ 50 = 2ab \\ ab = \frac{50}{2} = 25\\ \\ \\ now \: \\ ( {a + b})^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) \\ ( {10})^{3} = {a}^{3} + {b}^{3} + 3 \times 25 \times 10 \\ 1000 = {a}^{3} + {b}^{3} + 750 \\ {a}^{3} + {b}^{3} = 1000 - 750 \\ {a}^{3} + {b}^{3} = 250$