Question

Ajutor
2×25^x=10^x+4^x

Answer 1

Răspuns:

25ˣ=(5²)ˣ=5²ˣ

10ˣ=2ˣ*5ˣ

4ˣ=2²ˣ

Inlocuiesti si    obtii

2*5²ˣ=2ˣ*5ˣ+2²ˣ

Imparti   egalitatea     prin 5²ˣ

2*5²ˣ/5²ˣ=(2ˣ*5ˣ)/5²ˣ+2²ˣ/5²ˣ

2=2ˣ/5ˣ+(2²ˣ/5²ˣ)

(2/5)ˣ+(2/5)²ˣ=2

(2/5)ˣ=y   y>0

y+y²=2

y²+y-2=0

Δ=1²-4*(-2)=1+8=9

√Δ=√9=3

y1=(-1-3)/2=-4/2=-2<0 nu   convine problemei

y2=(-1+3)/2=2/2=1>0 se   accepta

(2/5)ˣ=1=>

x=0

Explicație pas cu pas: