Question

If x² + 4x-1=0 and x is positive then
find
the value of x +1 /x​

Answer 1

Step-by-step explanation:

x2+4x-1 =0

5x2-1=0

10x-1=0

10x=0-1

10x=1

x=10÷1=10

10+1÷10=11÷10

=1.1

Answer 2

Given equation -

${x}^{2} - 4x - 1 = 0$

$= > x = \frac{ - ( - 4) \pm \sqrt{ {4}^{2} - 4(1)( - 1)} }{2 \times 1}$

$= > \frac{4 \pm \sqrt{20} }{2}$

$= > \frac{4 \pm2 \sqrt{5} }{2}$

$= > {2 + \sqrt{5} }........ \: taking \: ony \: + ve \: value$

Therefore,

$x + \frac{1}{x} = 2 + \sqrt{5} + \frac{1}{2 + \sqrt{5} }$

on rationalising 1/2+√5 we get,

$x + \frac{1}{x} = 2 + \sqrt{5} + \sqrt{5} - 2$

$x + \frac{1}{x} = 2 \sqrt{5}$