Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2+6=0\)
2. \(-2(10x^2-2)=-(13x^2-4)\)
3. \(4x^2+576=0\)
4. \(-4x^2-10=-6x^2-10\)
5. \(-2(4x^2+2)=-(15x^2+4)\)
6. \(3x^2-1176=-4x^2+7\)
7. \(8x^2-308=5x^2-8\)
8. \(9x^2-113=8x^2+8\)
9. \(-12x^2+638=-4x^2-10\)
10. \(3(-5x^2-3)=-(13x^2+251)\)
11. \(7x^2-139=6x^2+5\)
12. \(-2(5x^2+8)=-(17x^2+863)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2+6=0 \\ \Leftrightarrow -6x^2 = -6 \\ \Leftrightarrow x^2 = \frac{-6}{-6}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
2. \(-2(10x^2-2)=-(13x^2-4) \\ \Leftrightarrow -20x^2+4=-13x^2+4 \\ \Leftrightarrow -20x^2+13x^2=4-4 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(4x^2+576=0 \\ \Leftrightarrow 4x^2 = -576 \\ \Leftrightarrow x^2 = \frac{-576}{4} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-4x^2-10=-6x^2-10 \\ \Leftrightarrow -4x^2+6x^2=-10+10 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(-2(4x^2+2)=-(15x^2+4) \\ \Leftrightarrow -8x^2-4=-15x^2-4 \\ \Leftrightarrow -8x^2+15x^2=-4+4 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(3x^2-1176=-4x^2+7 \\ \Leftrightarrow 3x^2+4x^2=7+1176 \\ \Leftrightarrow 7x^2 = 1183 \\ \Leftrightarrow x^2 = \frac{1183}{7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
7. \(8x^2-308=5x^2-8 \\ \Leftrightarrow 8x^2-5x^2=-8+308 \\ \Leftrightarrow 3x^2 = 300 \\ \Leftrightarrow x^2 = \frac{300}{3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
8. \(9x^2-113=8x^2+8 \\ \Leftrightarrow 9x^2-8x^2=8+113 \\ \Leftrightarrow x^2 = 121 \\ \Leftrightarrow x^2 = \frac{121}{1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(-12x^2+638=-4x^2-10 \\ \Leftrightarrow -12x^2+4x^2=-10-638 \\ \Leftrightarrow -8x^2 = -648 \\ \Leftrightarrow x^2 = \frac{-648}{-8}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(3(-5x^2-3)=-(13x^2+251) \\ \Leftrightarrow -15x^2-9=-13x^2-251 \\ \Leftrightarrow -15x^2+13x^2=-251+9 \\ \Leftrightarrow -2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{-2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
11. \(7x^2-139=6x^2+5 \\ \Leftrightarrow 7x^2-6x^2=5+139 \\ \Leftrightarrow x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{1}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
12. \(-2(5x^2+8)=-(17x^2+863) \\ \Leftrightarrow -10x^2-16=-17x^2-863 \\ \Leftrightarrow -10x^2+17x^2=-863+16 \\ \Leftrightarrow 7x^2 = -847 \\ \Leftrightarrow x^2 = \frac{-847}{7} < 0 \\ V = \varnothing \\ -----------------\)