Question

1. Aflati-l pe x din:
a) 3x+5=x+25 b) 27-3x=17-x
2. Stiind ca xy+xz=280 si y+z=7, calculati x.
3. Aflati x, stiind ca $3^{x}$+$3^{x+1}$+$3^{x+2}$=117
4. Aflati numerele naturale x, y, z stiind ca: x·y=6, y·z=21 si x·z=14

Answer 1

a) 3x+5=x+25
2x=20
x=10 

b) 27-3x=17-x
2x=10
x=5
2. Stiind ca xy+xz=280 si y+z=7, calculati x.
x(y+z)=280
7x=280
x=40

3. Aflati x, stiind ca 3^x+3^(x+1)+3^(x+2)=117
3^x ×(3⁰+3¹+3²)=117
3^x ×(1+3+9)=117
3^x ×13=117
3^x=117/13
3^x=9 = 3²
x=2

4. Aflati numerele naturale x, y, z stiind ca: x·y=6, y·z=21 si x·z=14
x·y=6      x=6/y
 y·z=21   z=21/y
 x·z=14
6/y · 21/y=14
126/y² =14
y²=9=3²
y=3