Question

If a2 + 1/a2= 23 find value of a3 + 1/a3

Answer 1

a²+1/a² = 23
a²+1/a²+2 = 25
we know that , a²+b²+2ab = (a+b)²
(a+1/a)² = 25
a+1/a = √25 = 5
a³+1/a³ = (a+1/a)(a²+1/a²-ab)

as we know that a³+ b ³= (a+b)(a²+b²-ab)
a³+1/a³ = 5(23-1)
a³+1/a³ = 5(22) => 110
hope this helps

Answer 2

Answer:

The value of a³+1/a³ = 110.

Step-by-step explanation:

Given:

a²+1/a² = 23

To find:

the value of a³+1/a³.

Step 1

Let, a²+1/a² = 23

then, a²+1/a²+2 = 25

we know that ,

By using Binomial expansion, we get

a²+b²+2ab = (a + b)²

(a+1/a)² = 25

Simplifying the above equation, we get

a+1/a = √25 = 5

Therefore, a+1/a = 5.

Step 2

By using Binomial expansion, we get

a³+1/a³ = (a+1/a)(a²+1/a²-ab)

We know that a³+ b³= (a + b)(a²+b²-ab)

a³+1/a³ = 5(23 - 1)

a³+1/a³ = 5(22)

a³+1/a³ = 110.

Therefore, the value of a³+1/a³ = 110.

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