Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(6x^2+486=0\)
2. \(7x^2+700=0\)
3. \(2(2x^2-5)=-(-3x^2+10)\)
4. \(5(7x^2-7)=-(-41x^2+131)\)
5. \(2(-9x^2-7)=-(10x^2+86)\)
6. \(5x^2-5=0\)
7. \(-4x^2+16=0\)
8. \(17x^2-80=9x^2-8\)
9. \(-3(-6x^2-4)=-(-11x^2+835)\)
10. \(-8x^2-128=0\)
11. \(-3(-5x^2+9)=-(-18x^2+102)\)
12. \(-14x^2+733=-8x^2+7\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(6x^2+486=0 \\ \Leftrightarrow 6x^2 = -486 \\ \Leftrightarrow x^2 = \frac{-486}{6} < 0 \\ V = \varnothing \\ -----------------\)
2. \(7x^2+700=0 \\ \Leftrightarrow 7x^2 = -700 \\ \Leftrightarrow x^2 = \frac{-700}{7} < 0 \\ V = \varnothing \\ -----------------\)
3. \(2(2x^2-5)=-(-3x^2+10) \\ \Leftrightarrow 4x^2-10=3x^2-10 \\ \Leftrightarrow 4x^2-3x^2=-10+10 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(5(7x^2-7)=-(-41x^2+131) \\ \Leftrightarrow 35x^2-35=41x^2-131 \\ \Leftrightarrow 35x^2-41x^2=-131+35 \\ \Leftrightarrow -6x^2 = -96 \\ \Leftrightarrow x^2 = \frac{-96}{-6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
5. \(2(-9x^2-7)=-(10x^2+86) \\ \Leftrightarrow -18x^2-14=-10x^2-86 \\ \Leftrightarrow -18x^2+10x^2=-86+14 \\ \Leftrightarrow -8x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-8}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
6. \(5x^2-5=0 \\ \Leftrightarrow 5x^2 = 5 \\ \Leftrightarrow x^2 = \frac{5}{5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
7. \(-4x^2+16=0 \\ \Leftrightarrow -4x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{-4}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
8. \(17x^2-80=9x^2-8 \\ \Leftrightarrow 17x^2-9x^2=-8+80 \\ \Leftrightarrow 8x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{8}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
9. \(-3(-6x^2-4)=-(-11x^2+835) \\ \Leftrightarrow 18x^2+12=11x^2-835 \\ \Leftrightarrow 18x^2-11x^2=-835-12 \\ \Leftrightarrow 7x^2 = -847 \\ \Leftrightarrow x^2 = \frac{-847}{7} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-8x^2-128=0 \\ \Leftrightarrow -8x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{-8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-3(-5x^2+9)=-(-18x^2+102) \\ \Leftrightarrow 15x^2-27=18x^2-102 \\ \Leftrightarrow 15x^2-18x^2=-102+27 \\ \Leftrightarrow -3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{-3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
12. \(-14x^2+733=-8x^2+7 \\ \Leftrightarrow -14x^2+8x^2=7-733 \\ \Leftrightarrow -6x^2 = -726 \\ \Leftrightarrow x^2 = \frac{-726}{-6}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)