Question

Find it plz
$if {x}^{2} + {y}^{2} = 90 \: and \: xy - 27 \: they \: find \: the \: value \: of \: {x}^{3} + {y}^{3}$

Answer 1

➡HERE IS YOUR ANSWER⬇

${x}^{2} + {y}^{2} = 90 \\ \\ or\: \: {(x + y)}^{2} - 2xy = 90 \\ \\ or \: \: {(x +y )}^{2} - 2.27 = 90 \: (since \: xy = 27) \\ \\ or \: \: {(x + y)}^{2} = 90 + 54 \\ \\ or \: \: {(x + y)}^{2} = 144 = {12}^{2} \\ \\ so \: \: (x + y) = 12 \: \: or \: \: (x + y) = - 12$

Again,

${x}^{3} + {y}^{3} \\ \\ = {(x + y)}^{3 } - 3xy(x + y)$

When, x +y = 12,

${x}^{3} + {y}^{3} \\ \\ = {12}^{3} - 3.27.12 \\ \\ = 1728 - 972 \\ \\ = 756$

When, x + y = - 12,

${x}^{3} + {y}^{3} \\ \\ = {( - 12)}^{3} - 3.27.( - 12) \\ \\ = - 1728 + 972 \\ \\ = - 756$

⬆HOPE THIS HELPS YOU⬅