Question

who can solve this problem​

Answer 1

${a}^{2} + {b}^{2} = 69 \\ {a}^{4} + {b}^{4} = 3904 \\ or { {(a }^{2} + {b}^{2} ) }^{2} - 2 {a}^{2} {b}^{2} = 3409 \\ or \: {(69)}^{2} - 2{a}^{2} {b}^{2} = 3409 \\ or \: {a}^{2} {b}^{2} = \frac{1352}{2} \\ or \: ab = 26 \\ \\ now \: {a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab \\ or \: 69 = {(a + b)}^{2} - 2 \times 26 \\ or \: (a + b ) = 11 \\ \\ so \: {a}^{3} + {b}^{3} = {(a + b)}^{3} - 3ab(a + b) \\ \: \: \: \: = {(11)}^{3} - 3 \times 26(11) \\ = 1331 - 858 \\ = 473$