Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2x^2-102=9x^2+10\)
2. \(-8x^2+1800=0\)
3. \(8x^2+104=6x^2+6\)
4. \(-3(2x^2+2)=-(14x^2-194)\)
5. \(6x^2-384=0\)
6. \(-3(6x^2+6)=-(16x^2-320)\)
7. \(-2(-6x^2-8)=-(-5x^2-23)\)
8. \(-9x^2+29=-8x^2-7\)
9. \(-x^2-65=-4x^2+10\)
10. \(-2x^2-38=6x^2-6\)
11. \(4(-8x^2+4)=-(35x^2-523)\)
12. \(8x^2-800=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2x^2-102=9x^2+10 \\ \Leftrightarrow 2x^2-9x^2=10+102 \\ \Leftrightarrow -7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{-7} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-8x^2+1800=0 \\ \Leftrightarrow -8x^2 = -1800 \\ \Leftrightarrow x^2 = \frac{-1800}{-8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
3. \(8x^2+104=6x^2+6 \\ \Leftrightarrow 8x^2-6x^2=6-104 \\ \Leftrightarrow 2x^2 = -98 \\ \Leftrightarrow x^2 = \frac{-98}{2} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-3(2x^2+2)=-(14x^2-194) \\ \Leftrightarrow -6x^2-6=-14x^2+194 \\ \Leftrightarrow -6x^2+14x^2=194+6 \\ \Leftrightarrow 8x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(6x^2-384=0 \\ \Leftrightarrow 6x^2 = 384 \\ \Leftrightarrow x^2 = \frac{384}{6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
6. \(-3(6x^2+6)=-(16x^2-320) \\ \Leftrightarrow -18x^2-18=-16x^2+320 \\ \Leftrightarrow -18x^2+16x^2=320+18 \\ \Leftrightarrow -2x^2 = 338 \\ \Leftrightarrow x^2 = \frac{338}{-2} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-2(-6x^2-8)=-(-5x^2-23) \\ \Leftrightarrow 12x^2+16=5x^2+23 \\ \Leftrightarrow 12x^2-5x^2=23-16 \\ \Leftrightarrow 7x^2 = 7 \\ \Leftrightarrow x^2 = \frac{7}{7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
8. \(-9x^2+29=-8x^2-7 \\ \Leftrightarrow -9x^2+8x^2=-7-29 \\ \Leftrightarrow -x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-1}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
9. \(-x^2-65=-4x^2+10 \\ \Leftrightarrow -x^2+4x^2=10+65 \\ \Leftrightarrow 3x^2 = 75 \\ \Leftrightarrow x^2 = \frac{75}{3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(-2x^2-38=6x^2-6 \\ \Leftrightarrow -2x^2-6x^2=-6+38 \\ \Leftrightarrow -8x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{-8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(4(-8x^2+4)=-(35x^2-523) \\ \Leftrightarrow -32x^2+16=-35x^2+523 \\ \Leftrightarrow -32x^2+35x^2=523-16 \\ \Leftrightarrow 3x^2 = 507 \\ \Leftrightarrow x^2 = \frac{507}{3}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
12. \(8x^2-800=0 \\ \Leftrightarrow 8x^2 = 800 \\ \Leftrightarrow x^2 = \frac{800}{8}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)