Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2+66=9x^2-6\)
2. \(7x^2-1372=0\)
3. \(-2(-5x^2-5)=-(-6x^2-686)\)
4. \(-x^2+0=0\)
5. \(8x^2-1152=0\)
6. \(14x^2-43=9x^2+2\)
7. \(-3x^2-101=-6x^2+7\)
8. \(3x^2-1581=-4x^2-6\)
9. \(6x^2+0=0\)
10. \(-5(-3x^2+3)=-(-8x^2+862)\)
11. \(2x^2+200=0\)
12. \(4(-9x^2-10)=-(34x^2+48)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2+66=9x^2-6 \\ \Leftrightarrow x^2-9x^2=-6-66 \\ \Leftrightarrow -8x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-8}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
2. \(7x^2-1372=0 \\ \Leftrightarrow 7x^2 = 1372 \\ \Leftrightarrow x^2 = \frac{1372}{7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
3. \(-2(-5x^2-5)=-(-6x^2-686) \\ \Leftrightarrow 10x^2+10=6x^2+686 \\ \Leftrightarrow 10x^2-6x^2=686-10 \\ \Leftrightarrow 4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
4. \(-x^2+0=0 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(8x^2-1152=0 \\ \Leftrightarrow 8x^2 = 1152 \\ \Leftrightarrow x^2 = \frac{1152}{8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
6. \(14x^2-43=9x^2+2 \\ \Leftrightarrow 14x^2-9x^2=2+43 \\ \Leftrightarrow 5x^2 = 45 \\ \Leftrightarrow x^2 = \frac{45}{5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
7. \(-3x^2-101=-6x^2+7 \\ \Leftrightarrow -3x^2+6x^2=7+101 \\ \Leftrightarrow 3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{3}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
8. \(3x^2-1581=-4x^2-6 \\ \Leftrightarrow 3x^2+4x^2=-6+1581 \\ \Leftrightarrow 7x^2 = 1575 \\ \Leftrightarrow x^2 = \frac{1575}{7}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
9. \(6x^2+0=0 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(-5(-3x^2+3)=-(-8x^2+862) \\ \Leftrightarrow 15x^2-15=8x^2-862 \\ \Leftrightarrow 15x^2-8x^2=-862+15 \\ \Leftrightarrow 7x^2 = -847 \\ \Leftrightarrow x^2 = \frac{-847}{7} < 0 \\ V = \varnothing \\ -----------------\)
11. \(2x^2+200=0 \\ \Leftrightarrow 2x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{2} < 0 \\ V = \varnothing \\ -----------------\)
12. \(4(-9x^2-10)=-(34x^2+48) \\ \Leftrightarrow -36x^2-40=-34x^2-48 \\ \Leftrightarrow -36x^2+34x^2=-48+40 \\ \Leftrightarrow -2x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)