Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(-4x^2-7)=-(-6x^2-464)\)
2. \(-4(6x^2+7)=-(28x^2+32)\)
3. \(13x^2-392=9x^2+8\)
4. \(-4(9x^2-6)=-(29x^2+39)\)
5. \(-8x^2+392=0\)
6. \(-2x^2+338=0\)
7. \(11x^2-10=3x^2-10\)
8. \(2(6x^2+3)=-(-17x^2+974)\)
9. \(2x^2-54=3x^2-5\)
10. \(-6x^2+3=-2x^2+3\)
11. \(2(6x^2-9)=-(-5x^2-990)\)
12. \(5x^2+14=2x^2+2\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(-4x^2-7)=-(-6x^2-464) \\ \Leftrightarrow 8x^2+14=6x^2+464 \\ \Leftrightarrow 8x^2-6x^2=464-14 \\ \Leftrightarrow 2x^2 = 450 \\ \Leftrightarrow x^2 = \frac{450}{2}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
2. \(-4(6x^2+7)=-(28x^2+32) \\ \Leftrightarrow -24x^2-28=-28x^2-32 \\ \Leftrightarrow -24x^2+28x^2=-32+28 \\ \Leftrightarrow 4x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{4} < 0 \\ V = \varnothing \\ -----------------\)
3. \(13x^2-392=9x^2+8 \\ \Leftrightarrow 13x^2-9x^2=8+392 \\ \Leftrightarrow 4x^2 = 400 \\ \Leftrightarrow x^2 = \frac{400}{4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
4. \(-4(9x^2-6)=-(29x^2+39) \\ \Leftrightarrow -36x^2+24=-29x^2-39 \\ \Leftrightarrow -36x^2+29x^2=-39-24 \\ \Leftrightarrow -7x^2 = -63 \\ \Leftrightarrow x^2 = \frac{-63}{-7}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
5. \(-8x^2+392=0 \\ \Leftrightarrow -8x^2 = -392 \\ \Leftrightarrow x^2 = \frac{-392}{-8}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
6. \(-2x^2+338=0 \\ \Leftrightarrow -2x^2 = -338 \\ \Leftrightarrow x^2 = \frac{-338}{-2}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
7. \(11x^2-10=3x^2-10 \\ \Leftrightarrow 11x^2-3x^2=-10+10 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(2(6x^2+3)=-(-17x^2+974) \\ \Leftrightarrow 12x^2+6=17x^2-974 \\ \Leftrightarrow 12x^2-17x^2=-974-6 \\ \Leftrightarrow -5x^2 = -980 \\ \Leftrightarrow x^2 = \frac{-980}{-5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
9. \(2x^2-54=3x^2-5 \\ \Leftrightarrow 2x^2-3x^2=-5+54 \\ \Leftrightarrow -x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{-1} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-6x^2+3=-2x^2+3 \\ \Leftrightarrow -6x^2+2x^2=3-3 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(2(6x^2-9)=-(-5x^2-990) \\ \Leftrightarrow 12x^2-18=5x^2+990 \\ \Leftrightarrow 12x^2-5x^2=990+18 \\ \Leftrightarrow 7x^2 = 1008 \\ \Leftrightarrow x^2 = \frac{1008}{7}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
12. \(5x^2+14=2x^2+2 \\ \Leftrightarrow 5x^2-2x^2=2-14 \\ \Leftrightarrow 3x^2 = -12 \\ \Leftrightarrow x^2 = \frac{-12}{3} < 0 \\ V = \varnothing \\ -----------------\)