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

Concept Introduction: The polynomials are fun to play with.

Given:

We have been Given:

$2x + y + 5 = 0$

To Find:

We have to Find: Prove that

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

Solution:

According to the problem, we know,

${a}^{3} + {b}^{3} + {c}^{3} = 3abc$

therefore using that,

${(2x)}^{3} + {(y)}^{3} + {5}^{3} = 3 \times 2x \times y \times 5\\ 8 {x}^{3} + {y}^{3} + 125 = 30xy \\ 8 {x}^{3} + {y}^{3} + 125 - 30xy = 0$

Hence Proved.

Final Answer:

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

hence Proved.

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