1.
[tex] \frac{2x+3}{x+2}=\frac{x-1}{x-2} \\ \\ ( 2x+3)(x-2)=(x-1)(x+2) \\ \\ 2 x^{2} -4x+3x-6=x^{2}+2x-x-2 \\ \\ 2 x^{2}-x-6= x^{2} +x-2 \\ \\ 2 x^{2}- x^{2} -x-x=-2+6 \\ \\ x^{2} -2x=4 \\ \\ x^{2} -2x-4=0 \\ \\ [/tex]
Δ=4+16=20
x1=(2+2√5)/2=1+√5 si x2=1-√5
2.
[tex] \sqrt[3]{64}+ \sqrt{18}-3 \sqrt{2} \\ \\ 64=2^{6} \\ \\ \sqrt[3]{ 2^{6} }=2^{2} =4 \\ \\ \sqrt{18}= \sqrt{2*3 ^{2} } =3 \sqrt{2} \\ \\ 4+3 \sqrt{2}- 3\sqrt{2} \\ \\ \sqrt[3]{64}+ \sqrt{18}-3 \sqrt{2} =4[/tex]
4 este numar natural
3.
pretul dupa 2 scumpiri este 693 lei daca
prima scumpire cu 5% , a doua cu 10%
mergem inapoi : dupa a 2 a scumpire cu 10%, pretul este 693
100%-10%=90%
daca 693 reprezinta.......100%
x reprezinta .........90%
x=(693×90):100=623,7 lei
dupa a 2 a scumpire pretul a fost 623,7 lei
prima scumpire a fost cu 5%
100%-5%=95%
daca 623,7 reprezinta.......100%
x reprezinta .........95%
x=(623,7×95):100=592,515 lei
deci pretul initial a fost 592,515 lei
4.
[tex]2^{-1}+2^{-2} =0,75 \\ \\ 2^{-1}= \frac{1}{2^{1}}= \frac{1}{2} ; 2^{-2} = \frac{1}{ 2^{2}} = \frac{1}{4} \\ \\ \frac{1}{2}+ \frac{1}{4}= \frac{2+1}{4}= \frac{3}{4} = 0,75[/tex]
=0,75
5.
(x-2)² - x² + 8 = 0⇒x² - 4x + 4 - x² + 8 = 0⇒- 4x = -8-4 ⇒ 4x = 12 ⇒ x = 12:4
⇒x = 3
6.
[tex]0 \leq \frac{x+1}{2} \leq 3[/tex]
[tex] 0 \leq \frac{x+1}{2} \\ \\0 \leq x+1 \\ \\ -1 \leq x \\ \\ x \geq -1[/tex]
x∈[-1,∞)
[tex] \frac{x+1}{2} \leq 3 \\ \\ x+1 \leq 2*3 \\ \\ x \leq 6-1 \\ \\ x \leq 5 [/tex]
x∈(-∞,5]
x∈[-1,∞)∩(-∞,5]⇒x∈[-1,5]
