Question

Sa se afle valoarea de adevăr a propoziției: {x/x€N, 5 la puterea 20x: ( 5 la puterea 5 ori 5 la puterea 20: 5 la puterea 8) totul pa puterea x=125}={x/x€N , 2x+ 4x+6x+...+20x=110} ✨URGENT✨!!!!

Answer 1

Răspuns:

5²⁰ˣ:(5⁵·5²⁰:5⁸)ˣ=125

5²⁰ˣ:(5⁵⁺²⁰⁻⁸)ˣ=5³

5²⁰ˣ:5¹⁷ˣ=5³

5²⁰ˣ⁻¹⁷ˣ=5³

avem aceeasi baza calculam exponentii

20x-17x=3

3x=3=>x=3/3=>x=1

2x+4x+6x+...+20x=110

2x(1+2+3+...+10)=110

2x·[(10·(10+1)]/2=110

2x·55=110

2x=110:55

2x=2

x=2/2=>x=1

Answer 2

Răspuns: Propozitia este adevarata

Explicație pas cu pas:

Buna!

$\bf \circledast~~ Primul~termen$

$\bf 5^{20x}:(5^{5}\cdot5^{20} :5^{8} )^{x}=125$

$\bf 5^{20x}:(5^{5+20} :5^{8} )^{x}=5^{3}$

$\bf 5^{20x}:(5^{25-8})^{x}=5^{3}$

$\bf 5^{20x}:5^{17x}=5^{3}$

$\bf 5^{20x-17x}=5^{3}$

$\bf 5^{3x}=5^{3} \implies 3x = 3~~~\bigg|:3\implies \boxed{\boxed{\bf x = 1}}$

$\bf \circledast~~Al~ doilea~ termen$

$\bf 2x+4x+6x+.....+20x=110$

$\bf 2x+4x+6x+8x+10x+12x+14x+16x+18x+20x=110$

$\bf 11x = 110~~\bigg|:110 \implies \boxed{\boxed{\bf x= 1}}$

$\bf Propozitia ~este~adevarata$

==pav38==