If a^2+1/a=4 , find the value of 2a^3 + 2/a^3 - Maths - Expansions

Question

If a^2+1/a=4 , find the value of 2a^3 + 2/a^3

Kavita Verma · Accepted Answer

Dear Student,

I am assuming that the question is 'if (a2+1)/a = 4,
find the value of 2a3 + 2/a3'

So, (a2+1)/a = 4 ⇒ a + 1/a = 4
⇒ 2a3 + 2/a3
⇒ 2(a3 + 1/a3)
⇒ 2(a + 1/a) ( a2 + 1/a2 - 1)
⇒ 2 * 4 * (a2 + 1/a2 + 2 - 2 - 1)
⇒ 8 * [(a + 1/a)2 - 3]
⇒ 8 * (16 - 3)
⇒ 8 * 13
⇒ 104

Regards,

If a^2+1/a=4 , find the value of 2a^3 + 2/a^3.