Question

Se considera numarul x∈R*. Daca x+ 1/x=3, calculati x²+1/x².

Answer 1

x+1/x=3
(x²+1)/x²=3
3x²=x²+1
3x²-x²=1
2x²=1
x=√1/2
x=√0,5
x²+1/x²=(√0,5)²+1/(√0,5)²=
0,5+1/0,5=(0,25+1)/0,5=1,25/0,5=2,5

Answer 2

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=5