Question

if a/b +b/a =2, then a³ -b³​

Answer 1

Step-by-step explanation:

a

3

−b

3

=0

Step-by-step explanation:

\begin{gathered}Given\\\frac{a}{b}+\frac{b}{a}=-1\end{gathered}

Given

b

a

+

a

b

=−1

Multiply each term by ab , we get

\implies a^{2}+b^{2}=-ab--(1)⟹a

2

+b

2

=−ab−−(1)

\begin{gathered}Now, a^{3}-b^{3}\\=(a-b)(a^{2}+ab+b^{2})\\=(a-b)(a^{2}+b^{2}+ab)\\=(a-b)(-ab+ab)\end{gathered}

Now,a

3

−b

3

=(a−b)(a

2

+ab+b

2

)

=(a−b)(a

2

+b

2

+ab)

=(a−b)(−ab+ab)

/* From (1)*/

=(a-b)\times 0=(a−b)×0

=0=0

Therefore,

a^{3}-b^{3}=0a

3

−b

3

=0