1T 2012 vår LØSNING

Opgave 1

a)

1) <tex> 8+2 \cdot 3 - 3^2 - (10-12)^2 = 8 + 6 - 9 -4 =1</tex>

2) <tex> \frac{9^{\frac 12} \cdot 3^{-3}}{(3^{-2})^3} = \frac{(3^2)^{\frac 12} \cdot 3^{-3}}{3^{-6}} = 3^{1-3+6} =3^4 = 81 </tex>

b)

<tex>5,5 \cdot 10^5 \cdot 6,0 \cdot 10^6 = 5,5 \cdot 6,0 \cdot 10^{11} =33,0 \cdot 10^{11} = 3,3 \cdot 10^{12} </tex>

c)

<tex>\left[{ x+2y =16 \\ 3x-y=6 }\right] \\ \left[{ x =16-2y \\ 3(16-2y)-y=6 }\right] \\ \left[{ x =16-2y \\ 48-6y-y=6 } \right] \\ \left[{ x =16-2y \\ y=7 } \right] \\ \left[{ x = 2 \\ y=7 } \right] </tex>

d)

<tex>2x-3=6- \frac 14x</tex>

Grafisk løsning

Man observerer at: x = 4