Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(-6x^2-4)=-(33x^2+8)\)
2. \(-x^2-26=-3x^2+6\)
3. \(2x^2+98=0\)
4. \(-x^2-1810=-9x^2-10\)
5. \(3(-8x^2-9)=-(30x^2-1149)\)
6. \(5(-3x^2-10)=-(16x^2-146)\)
7. \(-3x^2+75=0\)
8. \(-5(-2x^2-6)=-(-4x^2-6)\)
9. \(-3(-5x^2-10)=-(-9x^2-246)\)
10. \(13x^2-34=5x^2-2\)
11. \(16x^2-5=10x^2-5\)
12. \(5x^2+980=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(-6x^2-4)=-(33x^2+8) \\ \Leftrightarrow -30x^2-20=-33x^2-8 \\ \Leftrightarrow -30x^2+33x^2=-8+20 \\ \Leftrightarrow 3x^2 = 12 \\ \Leftrightarrow x^2 = \frac{12}{3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
2. \(-x^2-26=-3x^2+6 \\ \Leftrightarrow -x^2+3x^2=6+26 \\ \Leftrightarrow 2x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
3. \(2x^2+98=0 \\ \Leftrightarrow 2x^2 = -98 \\ \Leftrightarrow x^2 = \frac{-98}{2} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-x^2-1810=-9x^2-10 \\ \Leftrightarrow -x^2+9x^2=-10+1810 \\ \Leftrightarrow 8x^2 = 1800 \\ \Leftrightarrow x^2 = \frac{1800}{8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
5. \(3(-8x^2-9)=-(30x^2-1149) \\ \Leftrightarrow -24x^2-27=-30x^2+1149 \\ \Leftrightarrow -24x^2+30x^2=1149+27 \\ \Leftrightarrow 6x^2 = 1176 \\ \Leftrightarrow x^2 = \frac{1176}{6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
6. \(5(-3x^2-10)=-(16x^2-146) \\ \Leftrightarrow -15x^2-50=-16x^2+146 \\ \Leftrightarrow -15x^2+16x^2=146+50 \\ \Leftrightarrow x^2 = 196 \\ \Leftrightarrow x^2 = \frac{196}{1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
7. \(-3x^2+75=0 \\ \Leftrightarrow -3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{-3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
8. \(-5(-2x^2-6)=-(-4x^2-6) \\ \Leftrightarrow 10x^2+30=4x^2+6 \\ \Leftrightarrow 10x^2-4x^2=6-30 \\ \Leftrightarrow 6x^2 = -24 \\ \Leftrightarrow x^2 = \frac{-24}{6} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-3(-5x^2-10)=-(-9x^2-246) \\ \Leftrightarrow 15x^2+30=9x^2+246 \\ \Leftrightarrow 15x^2-9x^2=246-30 \\ \Leftrightarrow 6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{6}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
10. \(13x^2-34=5x^2-2 \\ \Leftrightarrow 13x^2-5x^2=-2+34 \\ \Leftrightarrow 8x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
11. \(16x^2-5=10x^2-5 \\ \Leftrightarrow 16x^2-10x^2=-5+5 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(5x^2+980=0 \\ \Leftrightarrow 5x^2 = -980 \\ \Leftrightarrow x^2 = \frac{-980}{5} < 0 \\ V = \varnothing \\ -----------------\)