Question

if 2 X + 3 Y = 26 and xy = 26 find the value of x cube + 27 y cube

Answer 1

$2x + 3y = 26 \\ \\ xy = 26 \\ \\ cobs \\ \\ {(2x + 3y)}^{3} = {26}^{3} \\ \\ 8 {x}^{3} + 27 {y}^{3} + 18xy(2x + 3y) = {26}^{3} \\ \\ 8 {x}^{3} + 27 {y}^{3} + 18 \times 26(26) = {26}^{3} \\ \\ 8 {x}^{3} + 27 {y}^{3} = {26}^{2} (26 - 18) \\ \\ 8 {x}^{3} + 27 {y}^{3} = 8 \times {26}^{2} \\ \\ 8 {x}^{3} + 27 {y}^{3} = 5408 \\ \\ we \: have \\ \\ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)$

hope it helps