Question

X is equal to 2 + root 3 then find the value of x minus one by X only

Answer 1

Given,

x=2+ √3

To find

x - 1/x

substitute the value of x

2+√3 - 1/(2+√3)

rationalize the denominator of the second term by taking conjugate

conjugate of 2+√3 is 2-√3

⇒2+√3+ 1/(2+√3) ×(2-√3)/(2-√3)

⇒2+√3 + (2-√3)/(4-3)............by identity a²-b² = (a+b)(a-b)

⇒2+√3+2-√3

    = 4