Question

1)Rezolvati inecuatiile:a) 5la puterea x-123=2; b) xy-3y=12
2)Rezolvati ecuatia: x+3x+5x+...+99x=2x+4x+....+100x-50

Answer 1

1.a) 5^x-123=2
5^x=125
=>x=3; deoarece 5*5*5=125
b)?
2.Duci totul din partea stanga in partea dreapta cu sens schimbat
0=2x-x+4x-3x+...+100x-99x-50 Il duci pe 50 in stanga si faci calcule
50=x+x+...+x 
50=100x
x=1/2

Answer 2

a. 5 la x 123=2
⇒5 la x=125
⇒5 la x=5³⇒5=5;
⇒x=3;
b. x·y-3·y=12
⇒y[x-3]=12
⇒12=1·12
⇒y=1;⇒x-3=12⇒x=15;
⇒12=2·6
⇒y=2⇒x-3=6⇒x=9;
⇒12=3·4
⇒y=3;⇒x-3=4⇒x=7;
⇒x,y∈[[1,15][2,9][4,7][7,4][9,2][15,1]];
c. x[1+3+5+...+99]=x[2+4+...+100]-50
⇒x[[1+2+3+...+99]-[2+4+6+...+98]=x[2[1+2+...+50]]-50
⇒x[4950-2[1+2+3+...+49]]=x[2·1275]-50
⇒x[4950-2·1225]=2550x-50
⇒x[4950-2550]=2550x-50
⇒2400x=2550x-50
⇒2550x-2400x=50
⇒150x=50
⇒x=150/50
⇒x=3;