Question

If a+1/a=5 then what is the value of a^5-1/a^5??​

Answer 1

The value of a+ \frac{1}{a}

a

1

= 5.38 , -5.45

Given:

a - \frac{1}{a}

a

1

=5

To find:

The vale of a+ \frac{1}{a}

a

1

=?

Explanation:

Given that

a - \frac{1}{a}

a

1

= 5

\frac{a^2 -1}{a}

a

a

2

−1

= 5

a² -1 =5a

a² - 5a -1 = 0

By solving above equation,

a = 5.19 and a = -0.19

Finding the value of a+ \frac{1}{a}

a

1

So the value of a+ \frac{1}{a}

a

1

= 5.19 + \frac{1}{5.19}

5.19

1

= 5.38

and a+ \frac{1}{a}

a

1

= (-0.19) + \frac{1}{(-0.19)}

(−0.19)

1

= -5.45

The value of a+ \frac{1}{a}

a

1

= 5.38 , -5.45