Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2+0=0\)
2. \(-2(-9x^2+5)=-(-21x^2+7)\)
3. \(2(5x^2-7)=-(-8x^2+12)\)
4. \(-8x^2+1152=0\)
5. \(-4x^2+324=0\)
6. \(4x^2+5=3x^2+4\)
7. \(12x^2+29=4x^2-3\)
8. \(3x^2-363=0\)
9. \(9x^2-38=4x^2+7\)
10. \(-4x^2+64=0\)
11. \(2x^2+209=-4x^2-7\)
12. \(-5x^2+180=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2+0=0 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-2(-9x^2+5)=-(-21x^2+7) \\ \Leftrightarrow 18x^2-10=21x^2-7 \\ \Leftrightarrow 18x^2-21x^2=-7+10 \\ \Leftrightarrow -3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{-3} < 0 \\ V = \varnothing \\ -----------------\)
3. \(2(5x^2-7)=-(-8x^2+12) \\ \Leftrightarrow 10x^2-14=8x^2-12 \\ \Leftrightarrow 10x^2-8x^2=-12+14 \\ \Leftrightarrow 2x^2 = 2 \\ \Leftrightarrow x^2 = \frac{2}{2}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
4. \(-8x^2+1152=0 \\ \Leftrightarrow -8x^2 = -1152 \\ \Leftrightarrow x^2 = \frac{-1152}{-8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
5. \(-4x^2+324=0 \\ \Leftrightarrow -4x^2 = -324 \\ \Leftrightarrow x^2 = \frac{-324}{-4}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
6. \(4x^2+5=3x^2+4 \\ \Leftrightarrow 4x^2-3x^2=4-5 \\ \Leftrightarrow x^2 = -1 \\ \Leftrightarrow x^2 = \frac{-1}{1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(12x^2+29=4x^2-3 \\ \Leftrightarrow 12x^2-4x^2=-3-29 \\ \Leftrightarrow 8x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{8} < 0 \\ V = \varnothing \\ -----------------\)
8. \(3x^2-363=0 \\ \Leftrightarrow 3x^2 = 363 \\ \Leftrightarrow x^2 = \frac{363}{3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(9x^2-38=4x^2+7 \\ \Leftrightarrow 9x^2-4x^2=7+38 \\ \Leftrightarrow 5x^2 = 45 \\ \Leftrightarrow x^2 = \frac{45}{5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
10. \(-4x^2+64=0 \\ \Leftrightarrow -4x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(2x^2+209=-4x^2-7 \\ \Leftrightarrow 2x^2+4x^2=-7-209 \\ \Leftrightarrow 6x^2 = -216 \\ \Leftrightarrow x^2 = \frac{-216}{6} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-5x^2+180=0 \\ \Leftrightarrow -5x^2 = -180 \\ \Leftrightarrow x^2 = \frac{-180}{-5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)