Question

अवयव पाडा: $a^3+\frac{8}{a^3}$

Answer 1

अवयव:

${x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} ) \\ \\ here \\ \\ x = a \\ \\ y = \frac{2}{a} \\ \\ {a}^{3} + {\bigg( \frac{2}{a}\bigg) }^{3} = \bigg(a + \frac{2}{a}\bigg)\bigg( {a}^{2} - a\bigg( \frac{2}{a}\bigg)+ {\bigg( \frac{2}{a} )}^{2} \bigg) \\ \\ =\bigg( \frac{ {a}^{2} + 2 }{a}\bigg)\bigg( {a}^{2} - 2 + \frac{4}{ {a}^{2} }\bigg )$
$a^3+\frac{8}{a^3} = \bigg(a + \frac{2}{a}\bigg )\bigg( {a}^{2} - 2 + \frac{4}{ {a}^{2} } \bigg)$