Question

If x= 2+ root 3 find the value of x²+ 1/x²​

Answer 1

14

Explanation:

If: x = 2 + √3

Then, x² +1/x² = ?

We know, (a+b)² = a²+b²+2ab

So a²+b² = (a+b)²-2ab.

Assuming a = x and b = 1/x, we can write the question as:

• (x+1/x)² - 2* x*1/x
• (x+1/x)²-2 ..1

Here 1/x = 1/2+√3

On rationalisation,

1/x = 2-√3/(2+√3)(2-√3)

As a²-b² = (a+b)(a-b),

• 1/x = 2-√3/2²-(√3)²
• 1/x = 2-√3/4-3 = 2-√3

On putting values in (1),

• (2+√3+2-√3)²-2

√3 gets eliminated,

• 4² -2
• 16-2 = 14

The solution is 14.