Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(3x^2-4)=-(-7x^2+8)\)
2. \(-6x^2-726=0\)
3. \(-10x^2+905=-6x^2+5\)
4. \(-6x^2+486=0\)
5. \(4x^2-484=0\)
6. \(2(-9x^2-3)=-(23x^2-39)\)
7. \(5x^2-389=-3x^2+3\)
8. \(5(10x^2+10)=-(-45x^2-55)\)
9. \(13x^2-290=5x^2-2\)
10. \(-2(10x^2+10)=-(19x^2+101)\)
11. \(-2x^2+206=6x^2+6\)
12. \(3x^2+21=9x^2-3\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(3x^2-4)=-(-7x^2+8) \\ \Leftrightarrow 6x^2-8=7x^2-8 \\ \Leftrightarrow 6x^2-7x^2=-8+8 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-6x^2-726=0 \\ \Leftrightarrow -6x^2 = 726 \\ \Leftrightarrow x^2 = \frac{726}{-6} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-10x^2+905=-6x^2+5 \\ \Leftrightarrow -10x^2+6x^2=5-905 \\ \Leftrightarrow -4x^2 = -900 \\ \Leftrightarrow x^2 = \frac{-900}{-4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
4. \(-6x^2+486=0 \\ \Leftrightarrow -6x^2 = -486 \\ \Leftrightarrow x^2 = \frac{-486}{-6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
5. \(4x^2-484=0 \\ \Leftrightarrow 4x^2 = 484 \\ \Leftrightarrow x^2 = \frac{484}{4}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
6. \(2(-9x^2-3)=-(23x^2-39) \\ \Leftrightarrow -18x^2-6=-23x^2+39 \\ \Leftrightarrow -18x^2+23x^2=39+6 \\ \Leftrightarrow 5x^2 = 45 \\ \Leftrightarrow x^2 = \frac{45}{5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
7. \(5x^2-389=-3x^2+3 \\ \Leftrightarrow 5x^2+3x^2=3+389 \\ \Leftrightarrow 8x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{8}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
8. \(5(10x^2+10)=-(-45x^2-55) \\ \Leftrightarrow 50x^2+50=45x^2+55 \\ \Leftrightarrow 50x^2-45x^2=55-50 \\ \Leftrightarrow 5x^2 = 5 \\ \Leftrightarrow x^2 = \frac{5}{5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(13x^2-290=5x^2-2 \\ \Leftrightarrow 13x^2-5x^2=-2+290 \\ \Leftrightarrow 8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
10. \(-2(10x^2+10)=-(19x^2+101) \\ \Leftrightarrow -20x^2-20=-19x^2-101 \\ \Leftrightarrow -20x^2+19x^2=-101+20 \\ \Leftrightarrow -x^2 = -81 \\ \Leftrightarrow x^2 = \frac{-81}{-1}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
11. \(-2x^2+206=6x^2+6 \\ \Leftrightarrow -2x^2-6x^2=6-206 \\ \Leftrightarrow -8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
12. \(3x^2+21=9x^2-3 \\ \Leftrightarrow 3x^2-9x^2=-3-21 \\ \Leftrightarrow -6x^2 = -24 \\ \Leftrightarrow x^2 = \frac{-24}{-6}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)