Question

If a+1/a=5,prove that a^3+1/a^3=110​

Answer 1

Answer:

The above equation is true

Step-by-step explanation:

Given that

$a + \frac{1}{a} = 5$

we have to prove

$a {}^{3} + \frac{1}{ {a}^{3} } = 110$

the above equation is in the form of

$( {a}^{3} + {b}^{3} )$

we know the formula is

$( {a + b)}^{3} - 3ab(a + b)$

Here a=a and b=

$\frac{1}{a}$

now we Get L. H. S

${a}^{3} + \frac{1}{ {a}^{3} } \\ = {(a + \frac{1}{a} }^{3} ) - 3a \times \frac{1}{a} (a + \frac{1}{a} ) \\ = {5}^{3} - 3(5) \\ = 125 - 15 \\ = 110$

so L. H. S=R. H. S