Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2-245=0\)
2. \(16x^2+720=10x^2-6\)
3. \(-4x^2+4=0\)
4. \(7x^2-503=4x^2+4\)
5. \(-14x^2+279=-6x^2-9\)
6. \(-6x^2+0=0\)
7. \(-8x^2+128=0\)
8. \(-x^2+1=0\)
9. \(-2(8x^2+7)=-(13x^2+689)\)
10. \(2(-10x^2-2)=-(18x^2+4)\)
11. \(14x^2+5=10x^2+5\)
12. \(x^2-100=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2-245=0 \\ \Leftrightarrow 5x^2 = 245 \\ \Leftrightarrow x^2 = \frac{245}{5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(16x^2+720=10x^2-6 \\ \Leftrightarrow 16x^2-10x^2=-6-720 \\ \Leftrightarrow 6x^2 = -726 \\ \Leftrightarrow x^2 = \frac{-726}{6} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-4x^2+4=0 \\ \Leftrightarrow -4x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
4. \(7x^2-503=4x^2+4 \\ \Leftrightarrow 7x^2-4x^2=4+503 \\ \Leftrightarrow 3x^2 = 507 \\ \Leftrightarrow x^2 = \frac{507}{3}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
5. \(-14x^2+279=-6x^2-9 \\ \Leftrightarrow -14x^2+6x^2=-9-279 \\ \Leftrightarrow -8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
6. \(-6x^2+0=0 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-8x^2+128=0 \\ \Leftrightarrow -8x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-8}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
8. \(-x^2+1=0 \\ \Leftrightarrow -x^2 = -1 \\ \Leftrightarrow x^2 = \frac{-1}{-1}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(-2(8x^2+7)=-(13x^2+689) \\ \Leftrightarrow -16x^2-14=-13x^2-689 \\ \Leftrightarrow -16x^2+13x^2=-689+14 \\ \Leftrightarrow -3x^2 = -675 \\ \Leftrightarrow x^2 = \frac{-675}{-3}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
10. \(2(-10x^2-2)=-(18x^2+4) \\ \Leftrightarrow -20x^2-4=-18x^2-4 \\ \Leftrightarrow -20x^2+18x^2=-4+4 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(14x^2+5=10x^2+5 \\ \Leftrightarrow 14x^2-10x^2=5-5 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(x^2-100=0 \\ \Leftrightarrow x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)