if-x-1-x-4-and-x-1-x-3-then-prove-that-4-5-

Question Number 148711 by Rankut last updated on 30/Jul/21

i f x + \frac{1}{x} = 4, a n d x - \frac{1}{x} = 3

t h e n p r o v e t h a t 4 = 5

Answered by liberty last updated on 30/Jul/21

x^{2} + \frac{1}{x^{2}} + 2 = 16 \Rightarrow x^{2} + \frac{1}{x^{2}} = 14

x^{2} + \frac{1}{x^{2}} - 2 = 9 \Rightarrow x^{2} + \frac{1}{x^{2}} = 11

then 14 = 11

Answered by liberty last updated on 30/Jul/21

x + \frac{1}{x} = 4

x - \frac{1}{x} = 3

\Rightarrow x = \frac{7}{2} \land \frac{1}{x} = \frac{1}{2}

\Rightarrow \frac{7}{2} = 2 or 7 = 4

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