Question

Pls please answer this question ​

Answer 1

Answer:

a 3 - b3 =(a-b) (a2+ab+b2)

Answer 2

Given :-

$\underline{\sf{\implies \frac{a}{b} +\frac{b}{a} = -1 \;\;\;\;\;\;(a,b=0)}}$

To find :-

$\underline{\sf{\implies Value \; of \; a^{3} - b^{3} }}$

Solution :-

Firstly taking LCM of the given fraction

$\sf{\implies \frac{a}{b} + \frac{b}{a}= \frac{(a)^{2} +(b)^{2} }{a \times b } }$

$\sf{\implies \; So, \; \frac{(a)^{2}+(b)^{2} }{a.b} = -1}$

$\sf{\implies (a)^{2}+ (b)^{2} = -ab }$

$\sf{\implies (a)^{2}+ (b)^{2} +ab = 0}$

Now taking the identity whose value we have to find

$\sf{\implies \: As \; we \; know\; that \;(x)^{3}- (y)^{3} = ( x-y)[(x)^{2} + (y)^{2} + xy ]}$

Using this identity :-

$\sf{\implies (a)^{3} - (b)^{3} = (a-b)[(a)^{2} + (b)^{2} + ab ]}$

Now we have already find out the value of $\underline{\sf{(a)^{2}+ (b)^{2} + ab = 0 }}$

So, Putting the value of this

$\sf{\implies (a)^{3} - (b)^{3} = (a-b)(0)}$

${\underline{\underline{\sf{\implies (a)^{3} -(b)^{3} = 0}}}}$

So the answer is 0 .