S1 2018 vår LØSNING

DEL1

Oppgave 1

a)

$2x^2-5x+1=x-3 \\ 2x^2-5x-x+1+3 = 0 \\ 2x^2-6x+4=0 \quad |:2 \\ x^2-3x+2=0$

Bruker abc-formelen $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$, $a=1$, $b=-3$, $c=2$.

$x=\frac{-(-3)\pm\sqrt{(-3)^2-4\cdot 1 \cdot 2}}{2\cdot1} \\ x=\frac{3\pm\sqrt{1}}{2} \\ x_1=\frac{3-1}{2} \vee x_2=\frac{3+1}{2} \\ x_1=1 \vee x_2=2$

b)

$2lg(x+7)=4 \quad |:2\\ lg(x+7)=2 \\ 10^{lg(x+7)}=10^2 \\ x+7 = 100 \\ x=93$

c)

$3\cdot2^{3x+2}=12\cdot2^6 \quad |:3 \\ 2^{3x+2} = 4\cdot 2^6 \quad |:2^6 \\ \frac{2^{3x+2}}{2^6} = 4 \\ 2^{3x+2-6}=4 \\ 2^{3x-4}=2^2 \\ 3x-4=2 \\ 3x=6 \\ x=2$