Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3x^2-108=0\)
2. \(3(3x^2-6)=-(-14x^2+18)\)
3. \(-11x^2+852=-6x^2+7\)
4. \(10x^2-480=4x^2+6\)
5. \(2x^2+450=0\)
6. \(12x^2-94=8x^2+6\)
7. \(-8x^2+1352=0\)
8. \(3x^2-3=0\)
9. \(-7x^2+0=0\)
10. \(10x^2+263=6x^2+7\)
11. \(4x^2-900=0\)
12. \(-3(9x^2+6)=-(20x^2-45)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3x^2-108=0 \\ \Leftrightarrow 3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{3}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
2. \(3(3x^2-6)=-(-14x^2+18) \\ \Leftrightarrow 9x^2-18=14x^2-18 \\ \Leftrightarrow 9x^2-14x^2=-18+18 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-11x^2+852=-6x^2+7 \\ \Leftrightarrow -11x^2+6x^2=7-852 \\ \Leftrightarrow -5x^2 = -845 \\ \Leftrightarrow x^2 = \frac{-845}{-5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
4. \(10x^2-480=4x^2+6 \\ \Leftrightarrow 10x^2-4x^2=6+480 \\ \Leftrightarrow 6x^2 = 486 \\ \Leftrightarrow x^2 = \frac{486}{6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
5. \(2x^2+450=0 \\ \Leftrightarrow 2x^2 = -450 \\ \Leftrightarrow x^2 = \frac{-450}{2} < 0 \\ V = \varnothing \\ -----------------\)
6. \(12x^2-94=8x^2+6 \\ \Leftrightarrow 12x^2-8x^2=6+94 \\ \Leftrightarrow 4x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{4}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
7. \(-8x^2+1352=0 \\ \Leftrightarrow -8x^2 = -1352 \\ \Leftrightarrow x^2 = \frac{-1352}{-8}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
8. \(3x^2-3=0 \\ \Leftrightarrow 3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(-7x^2+0=0 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(10x^2+263=6x^2+7 \\ \Leftrightarrow 10x^2-6x^2=7-263 \\ \Leftrightarrow 4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{4} < 0 \\ V = \varnothing \\ -----------------\)
11. \(4x^2-900=0 \\ \Leftrightarrow 4x^2 = 900 \\ \Leftrightarrow x^2 = \frac{900}{4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
12. \(-3(9x^2+6)=-(20x^2-45) \\ \Leftrightarrow -27x^2-18=-20x^2+45 \\ \Leftrightarrow -27x^2+20x^2=45+18 \\ \Leftrightarrow -7x^2 = 63 \\ \Leftrightarrow x^2 = \frac{63}{-7} < 0 \\ V = \varnothing \\ -----------------\)