Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2x^2-651=-6x^2-3\)
2. \(-12x^2+138=-4x^2+10\)
3. \(-3(-8x^2+8)=-(-25x^2-201)\)
4. \(9x^2-24=4x^2-4\)
5. \(-3(4x^2+6)=-(6x^2+744)\)
6. \(x^2+242=6x^2-3\)
7. \(-2(9x^2-9)=-(17x^2+126)\)
8. \(12x^2-2=9x^2-5\)
9. \(12x^2-2=5x^2+5\)
10. \(-4x^2-2=-10x^2-2\)
11. \(-2x^2+338=0\)
12. \(-5(7x^2+9)=-(30x^2+650)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2x^2-651=-6x^2-3 \\ \Leftrightarrow 2x^2+6x^2=-3+651 \\ \Leftrightarrow 8x^2 = 648 \\ \Leftrightarrow x^2 = \frac{648}{8}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
2. \(-12x^2+138=-4x^2+10 \\ \Leftrightarrow -12x^2+4x^2=10-138 \\ \Leftrightarrow -8x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-8}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
3. \(-3(-8x^2+8)=-(-25x^2-201) \\ \Leftrightarrow 24x^2-24=25x^2+201 \\ \Leftrightarrow 24x^2-25x^2=201+24 \\ \Leftrightarrow -x^2 = 225 \\ \Leftrightarrow x^2 = \frac{225}{-1} < 0 \\ V = \varnothing \\ -----------------\)
4. \(9x^2-24=4x^2-4 \\ \Leftrightarrow 9x^2-4x^2=-4+24 \\ \Leftrightarrow 5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
5. \(-3(4x^2+6)=-(6x^2+744) \\ \Leftrightarrow -12x^2-18=-6x^2-744 \\ \Leftrightarrow -12x^2+6x^2=-744+18 \\ \Leftrightarrow -6x^2 = -726 \\ \Leftrightarrow x^2 = \frac{-726}{-6}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
6. \(x^2+242=6x^2-3 \\ \Leftrightarrow x^2-6x^2=-3-242 \\ \Leftrightarrow -5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{-5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
7. \(-2(9x^2-9)=-(17x^2+126) \\ \Leftrightarrow -18x^2+18=-17x^2-126 \\ \Leftrightarrow -18x^2+17x^2=-126-18 \\ \Leftrightarrow -x^2 = -144 \\ \Leftrightarrow x^2 = \frac{-144}{-1}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
8. \(12x^2-2=9x^2-5 \\ \Leftrightarrow 12x^2-9x^2=-5+2 \\ \Leftrightarrow 3x^2 = -3 \\ \Leftrightarrow x^2 = \frac{-3}{3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(12x^2-2=5x^2+5 \\ \Leftrightarrow 12x^2-5x^2=5+2 \\ \Leftrightarrow 7x^2 = 7 \\ \Leftrightarrow x^2 = \frac{7}{7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
10. \(-4x^2-2=-10x^2-2 \\ \Leftrightarrow -4x^2+10x^2=-2+2 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-2x^2+338=0 \\ \Leftrightarrow -2x^2 = -338 \\ \Leftrightarrow x^2 = \frac{-338}{-2}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
12. \(-5(7x^2+9)=-(30x^2+650) \\ \Leftrightarrow -35x^2-45=-30x^2-650 \\ \Leftrightarrow -35x^2+30x^2=-650+45 \\ \Leftrightarrow -5x^2 = -605 \\ \Leftrightarrow x^2 = \frac{-605}{-5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)