Find a3 - 1-a3-if-a - 1-a - 5

A + 1/a = 5 ⇒(a +1/a)^3 = (5)^3 ⇒ a^3 + 1/a^3 + 3a ×1/a( a + 1/a) = 125 ⇒ a^3 + 1/a^3 + 3(5) = 125 [a + 1/a = 5] ⇒ a^3 + 1/a^3 + 15 = 125 ⇒ a^3 + 1/a^3 = 125 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Expansion of (x+y)^3

Find a3 + 1/a...

Question

Find $a^{3} + \frac{1}{a^{3}} i f a + \frac{1}{a} = 5$

Open in App

Solution

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

Suggest Corrections

Similar questions

Q. Find:

a^{3} + \frac{1}{a^{3}}

, if

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

Q. Find:

a^{3} - \frac{1}{a^{3}}

, if

a - \frac{1}{a} = 4

Find $a^{3} - \frac{1}{a^{3}} i f a - \frac{1}{a} = 4$

Q. If

a \neq 0

and

a - \frac{1}{a} = 4

, find:

a^{3} - \frac{1}{a^{3}}

Q. If

a + \frac{1}{a} = 4

and

a \neq 0

, find :

a^{3} + \frac{1}{a^{3}}

Join BYJU'S Learning Program

Find a3+1a3 if a+1a=5

a+1a=5⇒(a+1a)3=(5)3⇒a3+1a3+3a×1a(a+1a)=125⇒a3+1a3+3(5)=125 [a+1a=5]⇒a3+1a3+15=125⇒a3+1a3=125−15⇒a3+1a3=110.

Find $a^{3} + \frac{1}{a^{3}} i f a + \frac{1}{a} = 5$