Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2+331=6x^2-7\)
2. \(-6x^2+384=0\)
3. \(3(8x^2-3)=-(-17x^2+856)\)
4. \(4x^2-157=7x^2-10\)
5. \(8x^2+8=0\)
6. \(6x^2-384=0\)
7. \(6x^2-486=0\)
8. \(5x^2-5=0\)
9. \(-3(2x^2+10)=-(10x^2-6)\)
10. \(x^2-49=0\)
11. \(3x^2-192=0\)
12. \(-5(-2x^2+6)=-(-3x^2+30)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2+331=6x^2-7 \\ \Leftrightarrow 4x^2-6x^2=-7-331 \\ \Leftrightarrow -2x^2 = -338 \\ \Leftrightarrow x^2 = \frac{-338}{-2}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
2. \(-6x^2+384=0 \\ \Leftrightarrow -6x^2 = -384 \\ \Leftrightarrow x^2 = \frac{-384}{-6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
3. \(3(8x^2-3)=-(-17x^2+856) \\ \Leftrightarrow 24x^2-9=17x^2-856 \\ \Leftrightarrow 24x^2-17x^2=-856+9 \\ \Leftrightarrow 7x^2 = -847 \\ \Leftrightarrow x^2 = \frac{-847}{7} < 0 \\ V = \varnothing \\ -----------------\)
4. \(4x^2-157=7x^2-10 \\ \Leftrightarrow 4x^2-7x^2=-10+157 \\ \Leftrightarrow -3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{-3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(8x^2+8=0 \\ \Leftrightarrow 8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{8} < 0 \\ V = \varnothing \\ -----------------\)
6. \(6x^2-384=0 \\ \Leftrightarrow 6x^2 = 384 \\ \Leftrightarrow x^2 = \frac{384}{6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
7. \(6x^2-486=0 \\ \Leftrightarrow 6x^2 = 486 \\ \Leftrightarrow x^2 = \frac{486}{6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
8. \(5x^2-5=0 \\ \Leftrightarrow 5x^2 = 5 \\ \Leftrightarrow x^2 = \frac{5}{5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(-3(2x^2+10)=-(10x^2-6) \\ \Leftrightarrow -6x^2-30=-10x^2+6 \\ \Leftrightarrow -6x^2+10x^2=6+30 \\ \Leftrightarrow 4x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
10. \(x^2-49=0 \\ \Leftrightarrow x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
11. \(3x^2-192=0 \\ \Leftrightarrow 3x^2 = 192 \\ \Leftrightarrow x^2 = \frac{192}{3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
12. \(-5(-2x^2+6)=-(-3x^2+30) \\ \Leftrightarrow 10x^2-30=3x^2-30 \\ \Leftrightarrow 10x^2-3x^2=-30+30 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)