Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(2x^2-6)=-(-12x^2+812)\)
2. \(-5(-3x^2-6)=-(-17x^2-272)\)
3. \(5x^2+10=9x^2+10\)
4. \(-8x^2+512=0\)
5. \(x^2-1=0\)
6. \(2(5x^2+7)=-(-6x^2-270)\)
7. \(7x^2-7=0\)
8. \(3x^2-477=9x^2+9\)
9. \(2x^2-18=0\)
10. \(-3x^2+27=0\)
11. \(-3(-8x^2+10)=-(-26x^2-362)\)
12. \(3(-2x^2+4)=-(9x^2-120)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(2x^2-6)=-(-12x^2+812) \\ \Leftrightarrow 4x^2-12=12x^2-812 \\ \Leftrightarrow 4x^2-12x^2=-812+12 \\ \Leftrightarrow -8x^2 = -800 \\ \Leftrightarrow x^2 = \frac{-800}{-8}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
2. \(-5(-3x^2-6)=-(-17x^2-272) \\ \Leftrightarrow 15x^2+30=17x^2+272 \\ \Leftrightarrow 15x^2-17x^2=272-30 \\ \Leftrightarrow -2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{-2} < 0 \\ V = \varnothing \\ -----------------\)
3. \(5x^2+10=9x^2+10 \\ \Leftrightarrow 5x^2-9x^2=10-10 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-8x^2+512=0 \\ \Leftrightarrow -8x^2 = -512 \\ \Leftrightarrow x^2 = \frac{-512}{-8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(x^2-1=0 \\ \Leftrightarrow x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{1}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(2(5x^2+7)=-(-6x^2-270) \\ \Leftrightarrow 10x^2+14=6x^2+270 \\ \Leftrightarrow 10x^2-6x^2=270-14 \\ \Leftrightarrow 4x^2 = 256 \\ \Leftrightarrow x^2 = \frac{256}{4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
7. \(7x^2-7=0 \\ \Leftrightarrow 7x^2 = 7 \\ \Leftrightarrow x^2 = \frac{7}{7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
8. \(3x^2-477=9x^2+9 \\ \Leftrightarrow 3x^2-9x^2=9+477 \\ \Leftrightarrow -6x^2 = 486 \\ \Leftrightarrow x^2 = \frac{486}{-6} < 0 \\ V = \varnothing \\ -----------------\)
9. \(2x^2-18=0 \\ \Leftrightarrow 2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{2}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
10. \(-3x^2+27=0 \\ \Leftrightarrow -3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{-3}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
11. \(-3(-8x^2+10)=-(-26x^2-362) \\ \Leftrightarrow 24x^2-30=26x^2+362 \\ \Leftrightarrow 24x^2-26x^2=362+30 \\ \Leftrightarrow -2x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{-2} < 0 \\ V = \varnothing \\ -----------------\)
12. \(3(-2x^2+4)=-(9x^2-120) \\ \Leftrightarrow -6x^2+12=-9x^2+120 \\ \Leftrightarrow -6x^2+9x^2=120-12 \\ \Leftrightarrow 3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{3}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)