Respuesta :

tonb

Answer:

i) x=0 or x=1.

ii) x ≈ -0.4 or x ≈ 1.7.

Step-by-step explanation:

i) If you shape this equation to match the equation of the graph, you can solve it graphically.

3x² - 3x + 2 = 2 can be written as

3x² - 3x + 2 -3 = 2 -3

3x² - 3x - 1 = -1

Which maps to y = 3x² - 3x - 1 with y = -1.

So if you draw y=-1, which is a horizontal line, the intersections will be your solutions. By the looks of it, without calculating, the solutions are x=0 or x=1.

ii) This one is already in the shape of the graph.

It is y = 3x² - 3x - 1 with y = x+1.

Now you have to draw y = x+1, which is a straight line with slope 1, through the point (0,1).

The solutions are a bit harder to estimate: x ≈ -0.4 or x ≈ 1.7.

tramserran

Answer:  (i) x = 0, x = 1

               (ii) 1.7 or -0.4

Step-by-step explanation:

(i) Factor 3x² - 3x + 2 = 2

               3x² - 3x       = 0

               3x(x - 1)        = 0

               3x = 0      x - 1 = 0

                 x = 0           x = 1

(ii) Use quadratic formula

    3x² - 3x - 1 = x + 1

    3x² - 4x - 2 = 0

   a=3  b=-4  c=-2

[tex]x=\dfrac{=b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-4)\pm \sqrt{(-4)^2-4(3)(-2)}}{2(3)}\\\\\\.\quad =\dfrac{4\pm \sqrt{16+24}}{6}\\\\\\.\quad =\dfrac{4\pm \sqrt{40}}{6}\\\\\\.\quad =\dfrac{4\pm 2\sqrt{10}}{6}\\\\\\.\quad =\dfrac{2\pm \sqrt{10}}{3}\\\\\\.\quad = 1.72\qquad or\qquad -0.387[/tex]

   

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