Question

Solutia ecuatiei : a) 2x-5=7este
B) 3 pe x-1=x+1 pe 5
Va rog sa fie complet adica exemplu: 5+5+5= 10+5=15

Answer 1

$\rm a)~2x-5=7 \\ 2x=7+5 \\ 2x=12 \\ x= \frac{12}{2} \\ x=6 \\ \\ \underline{Solutie}:x=6.$

$\rm b)~ \frac{3}{x-1}= \frac{x+1}{5} \\ \\ (x-1)(x+1)=3 \cdot 5 \\ \\ x^{2} -1=15 \\ \\ x^{2} =16 \\ \\ x^{2} -16=0 \\ \\ (x+4)(x-4)=0 \Rightarrow x \in \{-4;4\}. \\ \\ \underline{Solutie}: x \in \{-4;4\}.$

Answer 2

a)2x-5=7
2x=7+5
x=12/2
x=6
verificare
2·6-5=7
12-5=7

b)
3/(x-1)=(x+1)/5
(x-1)(x+1)=3·5
x²-1=15
x²=15+1
x²=16
x₁=√16=4
x₂=-√16=-4
S={-4,4}

verificare
daca x=4
3/(4-1)=(4+1)/5
3/3=5/5
1=1

daca x=-4
3/(-4-1)=(-4+1)/5
3/-5=-3/5
-3/5=-3/5