Question

if t+1/t = 8 then find the value of t^3 +1/t^3

Answer 1

t+1/t=8
(t+1/t)³=t³+1/t³+3t*1/t(t+1/t)
8³=t³+1 /t³+3(8)
8³-24=question
512-24=488

Answer 2

Concept

Given two numbers a and b, the formula for the cube of their sum is

(a+b)³ = a³+ b³ + 3ab(a+b)

Given

t+1/t = 8

Find

we need to find the value of  t³+1 /t³

Solution

We have,

t+1/t = 8

Taking cube on both sides we get

(t+1/t)³= 8³

expanding left hand side of the equation using a + b whole cube formula we get

(t+1/t)³= t³+ 1/t³+ 3t*1/t (t+1/t)

Therefore,

8³ = t³+1 /t³+3(t+1/t)

⇒ 8³ = t³+1 /t³+3(8)

8³ = t³+1 /t³+ 24

8³-24= t³+1 /t³

512-24= t³+1 /t³

488 = t³+1 /t³

Thus the value of t³+1 /t³ is 488

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