Răspuns: Propozitia este adevarata
Explicație pas cu pas:
Buna!
[tex]\bf \circledast~~ Primul~termen[/tex]
[tex]\bf 5^{20x}:(5^{5}\cdot5^{20} :5^{8} )^{x}=125[/tex]
[tex]\bf 5^{20x}:(5^{5+20} :5^{8} )^{x}=5^{3}[/tex]
[tex]\bf 5^{20x}:(5^{25-8})^{x}=5^{3}[/tex]
[tex]\bf 5^{20x}:5^{17x}=5^{3}[/tex]
[tex]\bf 5^{20x-17x}=5^{3}[/tex]
[tex]\bf 5^{3x}=5^{3} \implies 3x = 3~~~\bigg|:3\implies \boxed{\boxed{\bf x = 1}}[/tex]
[tex]\bf \circledast~~Al~ doilea~ termen[/tex]
[tex]\bf 2x+4x+6x+.....+20x=110[/tex]
[tex]\bf 2x+4x+6x+8x+10x+12x+14x+16x+18x+20x=110[/tex]
[tex]\bf 11x = 110~~\bigg|:110 \implies \boxed{\boxed{\bf x= 1}}[/tex]
[tex]\bf Propozitia ~este~adevarata[/tex]
==pav38==
