Question

$if \: \frac{a}{b} \: + \frac{b}{a} = \:then \: {a}^{3} - \: {b}^{3 = }$
guies plz.. help me plz. ​

Answer 1

☆Correct Question :-

$\tt \: if \: \dfrac{a}{b} + \dfrac{b}{a} = 1 \: then \: find \: a^{3} + {b}^{3}$

☆Answer :-

$\mapsto\rm \dfrac{a}{b} + \dfrac{b}{a} = 1$

Now doing cross-Multiplication,

$\mapsto\rm \dfrac{a^{2} + b^{2} }{ab} =1$

Now, subtracting ab will give as 0 .

$\mapsto\rm a^{2} + b^{2} - ab =0$

Now , we need to know the formula ,

$\boxed { \pink{\sf{a}^{3} + {b}^{3} = \sf \: (a + b)( {a}^{2} + {b}^{2} - ab)}} {\green \star}$

Now finding ,

$\mapsto \sf{a}^{3} + {b}^{3} = \sf \: (a + b) \times 0$

$\mapsto \sf{a}^{3} + {b}^{3} = \sf \: a + b \times 0$

$\mapsto \sf{a}^{3} + {b}^{3} = \sf \bf \underline{\underline{0}}$

$\boxed{\rm \: hence \: verified} \dag$