Question

6. What should be added to 2x3 – y3 + 3y – 3 to get x3
+y3 + 2y + 1?
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Answer 1

Given equations are,

$2x^{3}- y^{3} + 3y -3$

$x^{3}+y^{3}+2y+1$

Let 'A' is added to first equation to get the second equation.

We get,

$2x^{3}- y^{3} + 3y -3+A=x^{3}+y^{3}+2y+1$

Except 'A' transpose all the terms from LHS to RHS.

We get,

$A=x^{3}+y^{3}+2y+1-(2x^{3}- y^{3} + 3y -3)$

$A=x^{3}+y^{3}+2y+1-2x^{3}+y^{3} -3y +3$

Add all the similar terms.

$A=-x^{3} +2y^{3} -y+4$

Therefore, $-x^{3} +2y^{3} -y+4$ is added to the first equation to get second equation.