x-1-x-2-05-x-

Question Number 204480 by EJJDJX last updated on 18/Feb/24

x + \frac{1}{x} = 2.05

x = ?

Commented by TonyCWX08 last updated on 19/Feb/24

x^{2} + 1 = 2.05 x

x^{2} - 2.05 x = = - 1

x^{2} - 2.05 x + {(\frac{2.05}{2})}^{2} = - 1 + {(\frac{2.05}{2})}^{2}

{(x - \frac{2.05}{2})}^{2} = 0.050625

x - 1.025 = \pm \sqrt{0.050625}

x = 1.025 \pm 0.225

x_{1} = 1.25 x_{2} = 0.8

Answered by MM42 last updated on 18/Feb/24

\frac{x^{2} + 1}{x} = \frac{41}{20} \Rightarrow 20 x^{2} - 41 x + 20 = 0

x = 1.25 & x = 0.8

Answered by BaliramKumar last updated on 19/Feb/24

x + \frac{1}{x} = 2.05 \dots \dots \dots \dots \dots (i)

x - \frac{1}{x} = \pm \sqrt{2 . 05^{2} - 4} = \pm \sqrt{4.2025 - 4}

x - \frac{1}{x} = \pm \sqrt{0.2025} = \pm 0.45

x - \frac{1}{x} = 0.45 \dots \dots \dots \dots \dots (i i)

x - \frac{1}{x} = - 0.45 \dots \dots \dots \dots \dots \dots \dots . . (i i i)

(i) + (i i)

2 x = 2.5 \Rightarrow x = 1.25

(i) + (i i i)

2 x = 1.6 \Rightarrow x = 0.8