Question

Daca x ∈ Z si $\frac{x+1}{5} = \frac{20}{x+1}$ , aflati x .

Answer 1

( x +1 ) · ( x +1 ) = 5 ·20 
x² + 2x + 1 = 100
x² + 2x - 99= 0
Δ = 4 + 4· 99=400 
x =( -2 -20 ) /2 = -22 /2 = -11 ∈ Z
x = ( -2 +20 ) /2 = 18 /2 = 9 ∈ Z

Answer 2

[x+1]·[x+1]=5·20
⇒[x+1]²=100
⇒[x+1]²=10²
⇒x+1=10
⇒x=10-1
⇒x=9∈Z⇔x∈Z;