Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4(-6x^2+5)=-(-23x^2+45)\)
2. \(-13x^2+837=-6x^2-10\)
3. \(4(7x^2-9)=-(-22x^2-1140)\)
4. \(-5x^2+0=0\)
5. \(2x^2-8=0\)
6. \(-10x^2-9=-2x^2-9\)
7. \(-2x^2-18=0\)
8. \(-3(3x^2+4)=-(11x^2-20)\)
9. \(7x^2-343=0\)
10. \(3x^2-192=0\)
11. \(2(6x^2+3)=-(-5x^2-118)\)
12. \(-2(-6x^2-5)=-(-13x^2-10)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4(-6x^2+5)=-(-23x^2+45) \\ \Leftrightarrow 24x^2-20=23x^2-45 \\ \Leftrightarrow 24x^2-23x^2=-45+20 \\ \Leftrightarrow x^2 = -25 \\ \Leftrightarrow x^2 = \frac{-25}{1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-13x^2+837=-6x^2-10 \\ \Leftrightarrow -13x^2+6x^2=-10-837 \\ \Leftrightarrow -7x^2 = -847 \\ \Leftrightarrow x^2 = \frac{-847}{-7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
3. \(4(7x^2-9)=-(-22x^2-1140) \\ \Leftrightarrow 28x^2-36=22x^2+1140 \\ \Leftrightarrow 28x^2-22x^2=1140+36 \\ \Leftrightarrow 6x^2 = 1176 \\ \Leftrightarrow x^2 = \frac{1176}{6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
4. \(-5x^2+0=0 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(2x^2-8=0 \\ \Leftrightarrow 2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
6. \(-10x^2-9=-2x^2-9 \\ \Leftrightarrow -10x^2+2x^2=-9+9 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-2x^2-18=0 \\ \Leftrightarrow -2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{-2} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-3(3x^2+4)=-(11x^2-20) \\ \Leftrightarrow -9x^2-12=-11x^2+20 \\ \Leftrightarrow -9x^2+11x^2=20+12 \\ \Leftrightarrow 2x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
9. \(7x^2-343=0 \\ \Leftrightarrow 7x^2 = 343 \\ \Leftrightarrow x^2 = \frac{343}{7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
10. \(3x^2-192=0 \\ \Leftrightarrow 3x^2 = 192 \\ \Leftrightarrow x^2 = \frac{192}{3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
11. \(2(6x^2+3)=-(-5x^2-118) \\ \Leftrightarrow 12x^2+6=5x^2+118 \\ \Leftrightarrow 12x^2-5x^2=118-6 \\ \Leftrightarrow 7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
12. \(-2(-6x^2-5)=-(-13x^2-10) \\ \Leftrightarrow 12x^2+10=13x^2+10 \\ \Leftrightarrow 12x^2-13x^2=10-10 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)