Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(-9x^2-2)=-(-19x^2-148)\)
2. \(17x^2-245=10x^2+7\)
3. \(-4(-6x^2-5)=-(-28x^2+80)\)
4. \(-x^2+142=-7x^2-8\)
5. \(-8x^2+38=-5x^2-10\)
6. \(5(10x^2+9)=-(-55x^2-765)\)
7. \(-12x^2-78=-10x^2-6\)
8. \(2(-3x^2+3)=-(4x^2+92)\)
9. \(6x^2+294=0\)
10. \(-x^2+225=0\)
11. \(-3x^2-609=3x^2-9\)
12. \(4x^2-16=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(-9x^2-2)=-(-19x^2-148) \\ \Leftrightarrow 18x^2+4=19x^2+148 \\ \Leftrightarrow 18x^2-19x^2=148-4 \\ \Leftrightarrow -x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{-1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(17x^2-245=10x^2+7 \\ \Leftrightarrow 17x^2-10x^2=7+245 \\ \Leftrightarrow 7x^2 = 252 \\ \Leftrightarrow x^2 = \frac{252}{7}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
3. \(-4(-6x^2-5)=-(-28x^2+80) \\ \Leftrightarrow 24x^2+20=28x^2-80 \\ \Leftrightarrow 24x^2-28x^2=-80-20 \\ \Leftrightarrow -4x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-4}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
4. \(-x^2+142=-7x^2-8 \\ \Leftrightarrow -x^2+7x^2=-8-142 \\ \Leftrightarrow 6x^2 = -150 \\ \Leftrightarrow x^2 = \frac{-150}{6} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-8x^2+38=-5x^2-10 \\ \Leftrightarrow -8x^2+5x^2=-10-38 \\ \Leftrightarrow -3x^2 = -48 \\ \Leftrightarrow x^2 = \frac{-48}{-3}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
6. \(5(10x^2+9)=-(-55x^2-765) \\ \Leftrightarrow 50x^2+45=55x^2+765 \\ \Leftrightarrow 50x^2-55x^2=765-45 \\ \Leftrightarrow -5x^2 = 720 \\ \Leftrightarrow x^2 = \frac{720}{-5} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-12x^2-78=-10x^2-6 \\ \Leftrightarrow -12x^2+10x^2=-6+78 \\ \Leftrightarrow -2x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{-2} < 0 \\ V = \varnothing \\ -----------------\)
8. \(2(-3x^2+3)=-(4x^2+92) \\ \Leftrightarrow -6x^2+6=-4x^2-92 \\ \Leftrightarrow -6x^2+4x^2=-92-6 \\ \Leftrightarrow -2x^2 = -98 \\ \Leftrightarrow x^2 = \frac{-98}{-2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
9. \(6x^2+294=0 \\ \Leftrightarrow 6x^2 = -294 \\ \Leftrightarrow x^2 = \frac{-294}{6} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-x^2+225=0 \\ \Leftrightarrow -x^2 = -225 \\ \Leftrightarrow x^2 = \frac{-225}{-1}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
11. \(-3x^2-609=3x^2-9 \\ \Leftrightarrow -3x^2-3x^2=-9+609 \\ \Leftrightarrow -6x^2 = 600 \\ \Leftrightarrow x^2 = \frac{600}{-6} < 0 \\ V = \varnothing \\ -----------------\)
12. \(4x^2-16=0 \\ \Leftrightarrow 4x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{4}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)