Question

If a+1/a=3What is the answer? a⁵+1/a⁵​

Answer 1

Answer:

123

Step-by-step explanation:

We can square and cube the equation, then multiply the results together.

(a + $\frac{1}{a}$) = 3 ← square both sides

a² + 2 + $\frac{1}{a^2}$ = 9 ( subtract 2 from both sides )

a² + $\frac{1}{a^2}$ = 7 → (1)

-----------------------

Now cube both sides

a³ + $\frac{1}{a^3}$ + 3(a + $\frac{1}{a}$) = 27

a³ + $\frac{1}{a^3}$ + 3(3) = 27

a³ + $\frac{1}{a^3}$ + 9 = 27 ( subtract 9 from both sides )

a³ + $\frac{1}{a^3}$ = 18 → (2)

------------------------------

Multiply (1) and (2)

(a² + $\frac{1}{a^2}$ )(a³ + $\frac{1}{a^3}$ ) = 7(18)

$a^{5}$  + ( $\frac{1}{a}$ + a) + $\frac{1}{a^5}$ = 126

$a^{5}$ + 3 + $\frac{1}{a^5}$ = 126 ( subtract 3 from both sides )

$a^{5}$ + $\frac{1}{a^5}$ = 123