Question

cum se fac exercitiile de tipul x-1/x = n x^2-1/x^2

Answer 1

x -1/x = n ;   ridicam la patrat

(x -1/x)²=n²

x² - 2•x•1/x + 1/x²=n²

x² - 2 + 1/x²=n²

x² + 1/x²=n²+2

x²+2+ 1/x²=n²+4; (am adunat 2 in fiecare parte)

(x+ 1/x)²= n²+4

x+ 1/x= +/- √(n²+4)

x²- 1/x²=(x-1/x)(x+1/x)

x²- 1/x²=+/- n•√(n²+4)