Question

If 2x + y = - 5, prove that 8x3 + y3– 30xy + 125 = 0

Answer 1

2x+y=-5,

2x+y+5=0,

 if a³+b³+c³=0,then a³+b³+c³=3abc,

So, 2x³+y³+5³=2x×3×y×5

  8x³+y³+125=30xy

  8x³+y³+125-30xy=0

Answer 2

Answer:

$2x + y= - 5(given)$

$cubing \: on \: both \: sides$

${(a + b ) }^{3} = {a}^{3 } + {b}^{3} + 3ab(a + b)$

${(2x)}^{3} + {y}^{3} + 3 \times 2x \times y(2x + y) = - 125$

$8 {x}^{3} + {y}^{3} + 6xy( - 5) + 125 = 0$

$8 {x}^{3} + {y}^{3} - 30xy + 125 = 0$

$hence \: proved.$