Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(-2x^2+7)=-(-10x^2+5)\)
2. \(12x^2-1362=4x^2-10\)
3. \(-5x^2+13=-6x^2+9\)
4. \(2(4x^2+5)=-(-11x^2-685)\)
5. \(11x^2+313=6x^2-7\)
6. \(7x^2-175=0\)
7. \(5(-2x^2+4)=-(3x^2+323)\)
8. \(5(6x^2-8)=-(-33x^2+28)\)
9. \(5x^2-674=9x^2+2\)
10. \(6x^2-1176=0\)
11. \(-2x^2+450=0\)
12. \(4(-2x^2-3)=-(2x^2-138)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(-2x^2+7)=-(-10x^2+5) \\ \Leftrightarrow 6x^2-21=10x^2-5 \\ \Leftrightarrow 6x^2-10x^2=-5+21 \\ \Leftrightarrow -4x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{-4} < 0 \\ V = \varnothing \\ -----------------\)
2. \(12x^2-1362=4x^2-10 \\ \Leftrightarrow 12x^2-4x^2=-10+1362 \\ \Leftrightarrow 8x^2 = 1352 \\ \Leftrightarrow x^2 = \frac{1352}{8}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
3. \(-5x^2+13=-6x^2+9 \\ \Leftrightarrow -5x^2+6x^2=9-13 \\ \Leftrightarrow x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{1} < 0 \\ V = \varnothing \\ -----------------\)
4. \(2(4x^2+5)=-(-11x^2-685) \\ \Leftrightarrow 8x^2+10=11x^2+685 \\ \Leftrightarrow 8x^2-11x^2=685-10 \\ \Leftrightarrow -3x^2 = 675 \\ \Leftrightarrow x^2 = \frac{675}{-3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(11x^2+313=6x^2-7 \\ \Leftrightarrow 11x^2-6x^2=-7-313 \\ \Leftrightarrow 5x^2 = -320 \\ \Leftrightarrow x^2 = \frac{-320}{5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(7x^2-175=0 \\ \Leftrightarrow 7x^2 = 175 \\ \Leftrightarrow x^2 = \frac{175}{7}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
7. \(5(-2x^2+4)=-(3x^2+323) \\ \Leftrightarrow -10x^2+20=-3x^2-323 \\ \Leftrightarrow -10x^2+3x^2=-323-20 \\ \Leftrightarrow -7x^2 = -343 \\ \Leftrightarrow x^2 = \frac{-343}{-7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
8. \(5(6x^2-8)=-(-33x^2+28) \\ \Leftrightarrow 30x^2-40=33x^2-28 \\ \Leftrightarrow 30x^2-33x^2=-28+40 \\ \Leftrightarrow -3x^2 = 12 \\ \Leftrightarrow x^2 = \frac{12}{-3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(5x^2-674=9x^2+2 \\ \Leftrightarrow 5x^2-9x^2=2+674 \\ \Leftrightarrow -4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{-4} < 0 \\ V = \varnothing \\ -----------------\)
10. \(6x^2-1176=0 \\ \Leftrightarrow 6x^2 = 1176 \\ \Leftrightarrow x^2 = \frac{1176}{6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
11. \(-2x^2+450=0 \\ \Leftrightarrow -2x^2 = -450 \\ \Leftrightarrow x^2 = \frac{-450}{-2}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
12. \(4(-2x^2-3)=-(2x^2-138) \\ \Leftrightarrow -8x^2-12=-2x^2+138 \\ \Leftrightarrow -8x^2+2x^2=138+12 \\ \Leftrightarrow -6x^2 = 150 \\ \Leftrightarrow x^2 = \frac{150}{-6} < 0 \\ V = \varnothing \\ -----------------\)