S1 2015 høst LØSNING

Oppgave 1

a)

$2x^2-3x=0 \\x(2x-3)= 0 \\ x=0 \vee x = \frac 32$

b)

$2^{3x+1} = 4^{17} \\ 2^{3x+1} = 2^{34} \\ 3x+1 = 34 \\ x = 11$

c)

$lg(2x+2) = 3 + lg2 \\ lg(2x+2) = lg(1000\cdot 2) \\ 2x= 1998 \\ x= 999$

Oppgave 2

a)

$\frac{8a^3(a^{-1}b)^2}{(2ab)^2}= \\ \frac{2^3a^3a^{-2}b^2}{2^2a^2b^2} = \\ 2^{3-2}a^{3-2-2}b^{2-2} = \\ 2a^{-1} = \\ \frac2a$

b)

$(x+y)(x-y) + (y+x) (y-x) - (x+y)(x-y)= \\ y^2-x^2$

Oppgave 3

<math> \left[ \begin{align*} 2x^2+x+y=7\\ 3x+y=-5 \end{align*}\right] </math>