Question

4+6+8+10+12+14+16+...+90+x=3+5+7+9+11+...+91 rezolați ecuatia va rog

Answer 1

4+6+8+...+90+x=3+5+7+...+91

Luam sumele si le calculam fara x .

S=4+6+8+...+90
S=90+...+8+6+4
--------------------------
⇒2S=94+94+...+94
Numar termeni: (90-4)/2+1=86/2+1=43+1=44
S=94x44/2
⇒S=47x44
⇒S=2068

A=3+5+7+...+91
A=91+...+7+5+3
-----------------------------
⇒2A=94+94+...+94
Numar termeni : (91-3)/2+1=88/2+1=44+1=45
A=45x94/2
⇒A=45x47
⇒A=2115

S+x=A
⇒2068+x=2115
⇒x=2115-2068
⇒x=47


Sper ca te-am ajutat ! :)