7)
a) 2(x+5)+5=25
2x+2*5+5=25
2x+15=25
2x=25-15
2x=10
x=10/2=5 care verifica conditia de a fi numar natural
b) x nu poate fi 0, deoarece este pe pozitia zecilor, deci poate lua valori intre 1 si 9 (*)
Daca x apartine {2,3,..,9} => x7 > 25 pentru orice x (**)
Din (*) si (**) => x=1
c)
[tex]\frac{3}{8} \leq \frac{6}{2a+1} \leq \frac{2}{3}\\\\\frac{8}{3} \geq \frac{2a+1}{6} \geq \frac{3}{2}\\\frac{8*6}{3} \geq 2a+1 \geq \frac{3*6}{2}\\\\16 \geq 2a+1 \geq 9\\\\15 \geq 2a \geq 8\\\\\frac{15}{2} \geq a \geq 4\\[/tex]
a apartine intervalului [4;15/2]
8)x=360 si y=420
a)
x=360=180*2=90*2*2=45*2*2*2=9*5*2*2*2=5*(3^2)*(2^3)
y=420=2*210=2*2*105=2*2*5*21=2*2*5*3*7=(2^2)*3*5*7
b) cmmdc al nr x si y
Se aleg factorii comuni la puterea cea mai mica:
(2^2)*(3^1)*(5^1)=4*3*5=60 =>cmmdc(x,y)=60
c)cmmmc al nr x si y
Se aleg factorii cu puterea cea mai mare
cmmmc(x,y)=(2^3)*(3^2)*(5^1)*(7^1)=2520
