Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3x^2-598=2x^2+7\)
2. \(-4x^2+4=0\)
3. \(3x^2-172=2x^2-3\)
4. \(-3x^2+156=-5x^2-6\)
5. \(5x^2+10=6x^2+10\)
6. \(-8x^2+128=0\)
7. \(-4(-9x^2+6)=-(-40x^2-652)\)
8. \(-3x^2+108=0\)
9. \(-2(2x^2-8)=-(-4x^2+632)\)
10. \(17x^2+126=9x^2-2\)
11. \(3(-10x^2+8)=-(35x^2-524)\)
12. \(-x^2-718=-7x^2+8\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3x^2-598=2x^2+7 \\ \Leftrightarrow -3x^2-2x^2=7+598 \\ \Leftrightarrow -5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{-5} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-4x^2+4=0 \\ \Leftrightarrow -4x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
3. \(3x^2-172=2x^2-3 \\ \Leftrightarrow 3x^2-2x^2=-3+172 \\ \Leftrightarrow x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
4. \(-3x^2+156=-5x^2-6 \\ \Leftrightarrow -3x^2+5x^2=-6-156 \\ \Leftrightarrow 2x^2 = -162 \\ \Leftrightarrow x^2 = \frac{-162}{2} < 0 \\ V = \varnothing \\ -----------------\)
5. \(5x^2+10=6x^2+10 \\ \Leftrightarrow 5x^2-6x^2=10-10 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(-8x^2+128=0 \\ \Leftrightarrow -8x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-8}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
7. \(-4(-9x^2+6)=-(-40x^2-652) \\ \Leftrightarrow 36x^2-24=40x^2+652 \\ \Leftrightarrow 36x^2-40x^2=652+24 \\ \Leftrightarrow -4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{-4} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-3x^2+108=0 \\ \Leftrightarrow -3x^2 = -108 \\ \Leftrightarrow x^2 = \frac{-108}{-3}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
9. \(-2(2x^2-8)=-(-4x^2+632) \\ \Leftrightarrow -4x^2+16=4x^2-632 \\ \Leftrightarrow -4x^2-4x^2=-632-16 \\ \Leftrightarrow -8x^2 = -648 \\ \Leftrightarrow x^2 = \frac{-648}{-8}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(17x^2+126=9x^2-2 \\ \Leftrightarrow 17x^2-9x^2=-2-126 \\ \Leftrightarrow 8x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(3(-10x^2+8)=-(35x^2-524) \\ \Leftrightarrow -30x^2+24=-35x^2+524 \\ \Leftrightarrow -30x^2+35x^2=524-24 \\ \Leftrightarrow 5x^2 = 500 \\ \Leftrightarrow x^2 = \frac{500}{5}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
12. \(-x^2-718=-7x^2+8 \\ \Leftrightarrow -x^2+7x^2=8+718 \\ \Leftrightarrow 6x^2 = 726 \\ \Leftrightarrow x^2 = \frac{726}{6}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)