Question

Se considera un numar real nenul x,astfel incat x+1/x=2.Aratati ca x²+1/x²=2
Va rog frumos sa ma ajutati!

Answer 1

$x+\frac{1}{x} = 2\,\big|^2$ (Ridic la pătrat)

$\Rightarrow \left(x+\frac{1}{x}\right)^2 = 2^2$

$\Rightarrow x^2+2\cdot x\cdot \frac{1}{x}+\left(\frac{1}{x}\right)^2 = 4$

$\Rightarrow x^2+2\cdot 1+\frac{1}{x^2} = 4$

$\Rightarrow x^2+2+\frac{1}{x^2} = 4$

$\Rightarrow x^2+\frac{1}{x^2} = 4-2$

$\Rightarrow x^2+\frac{1}{x^2} = 2\,\,\,\,\checkmark$

Answer 2

Explicație pas cu pas:

x+1/x=2  /²

x²+(1/x)²=4

extragem sub forma de formula :

(x+1/x)²=4

x²+2·x·1/x + (1/x)²=4

x²+2x/x+1/x²=4

x²+2+1/x²=4

x²+1/x²=4-2

x²+1/x²=2  (A)