Question

If x=4+2√3 find √x+1/√x​

Answer 1

Answer:

x = 7+4√3

To find √x we proceed,

√x = √(7+4√3)

√x = √(7+2x2√3)

√x = √(7+2√3x4)

√x = √(3+4+2√3x4)….. {writing 7 = 3+4}

If we observe RHS of √x we observe form of

√(a² + b² +2ab) where a=√3 and b =√4

Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3

√x = 2+√3

1/√x = 1/(2+√3)

Multiplying both numerator and denominator by 2 - √3, we get

1/√x = (2-√3)/(2-√3)(2+√3) = (2-√3)/(2²-√3²) =

1/√x = 2-√3

Hence √x +1/√x = 2+√3 +2 -√3 = 4

Answer 2

$\huge\pink{Answer}$

Given :

$x + = 2 + \sqrt{3}$

To find : find the value of

$x + \frac{1}{x}$

Since x =

$2 + \sqrt{3}$

$\frac{1}{x} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} }$

$\frac{1}{x} = \frac{2 - \sqrt{3} }{ {2}^{2} - \sqrt{ {3}^{2} } }$

$\frac{1}{x} = \frac{2 - \sqrt{3} }{4 - 3}$

$\frac{1}{x} = 2 - \sqrt{3}$

Substitute the values

$x + \frac{1}{x}$

$2 + \sqrt{3} + 2 - \sqrt{3}$

$= 4$

Hence , the value of x + 1/x is 4 .

$\huge\pink{hope \ \: it \: will \: help \: you}$