Question

If (x +(1/x)) = 2, then find the value of (x⁵ + x⁴ + x³ + x² + x + 1)

Answer 1

Correct Answer - Option 4 : 6

Given

(x +(1/x)) = 2,

(x5 + x4 + x3 + x2 + x + 1) = ?

Calculation

⇒ (x +(1/x)) = 2

⇒ (x² + 1)/x = 2

⇒ x² + 1 = 2x 

⇒ x² - 2x + 1² = 0

⇒ (x - 1)² = 0 

⇒ x = 1 

Now, Put the value in the given equation

⇒ (x5 + x4 + x3 + x2 + x + 1) = (1⁵ + 1⁴ + 1³ + 1² + 1 + 1)

⇒ (x5 + x4 + x3 + x2 + x + 1) = 6

∴ (x5 + x4 + x3 + x2 + x + 1) = 6 

Alternate method

(x +(1/x)) = 2

In this type of question in which x +(1/x)) = 2,

You can directly put value of x = 1 

When you put x = 1 

⇒ x +(1/x)) = 2 

i.e R.H.S = L.HS

So, put the value of x = 1 in the equation

⇒ (x5 + x4 + x3 + x2 + x + 1) = 6

∴ (x5 + x4 + x3 + x2 + x + 1) = 6