Question

x-1/x=3
x*2(x la puterea a doua) + 1/x*2=?

Answer 1

(x-1)/x=3
x-1=3x
2x=-1
x=-1/2
(x²+1)/x²=
[(-1/2)²+1]/(-1/2)²=
=[(1/4+1]/(1/4)=
=5/4×4/1=5

varianta cu x in afara fractiei
x-1/x=3
x²-2×x×1/x+1/x²=9
x²-2+1/x²=9
x²+1/x²=11

Answer 2

[tex]x-\frac{1}{x}=3\\ Ridicam\ la\ patrat:\\ (x-\frac{1}{x})^2=3^2\\ x^2-2\cdot x\cdot\frac{1}{x}+\frac{1}{x^2}=9\\ x^2+\frac{1}{x^2}-2=9\\ x^2+\frac{1}{x^2}=11\\ [/tex]