Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(-9x^2+4)=-(-32x^2+12)\)
2. \(-2(-5x^2+3)=-(-14x^2+6)\)
3. \(-5x^2-4=-6x^2-4\)
4. \(-6x^2+145=-9x^2-2\)
5. \(4(-7x^2+5)=-(33x^2-740)\)
6. \(-2x^2+72=0\)
7. \(2(8x^2+10)=-(-15x^2-189)\)
8. \(3(10x^2+3)=-(-25x^2-29)\)
9. \(-2(2x^2+6)=-(12x^2+660)\)
10. \(15x^2+964=7x^2-4\)
11. \(-x^2+19=6x^2-9\)
12. \(5(10x^2+8)=-(-48x^2-282)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(-9x^2+4)=-(-32x^2+12) \\ \Leftrightarrow 27x^2-12=32x^2-12 \\ \Leftrightarrow 27x^2-32x^2=-12+12 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-2(-5x^2+3)=-(-14x^2+6) \\ \Leftrightarrow 10x^2-6=14x^2-6 \\ \Leftrightarrow 10x^2-14x^2=-6+6 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-5x^2-4=-6x^2-4 \\ \Leftrightarrow -5x^2+6x^2=-4+4 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-6x^2+145=-9x^2-2 \\ \Leftrightarrow -6x^2+9x^2=-2-145 \\ \Leftrightarrow 3x^2 = -147 \\ \Leftrightarrow x^2 = \frac{-147}{3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(4(-7x^2+5)=-(33x^2-740) \\ \Leftrightarrow -28x^2+20=-33x^2+740 \\ \Leftrightarrow -28x^2+33x^2=740-20 \\ \Leftrightarrow 5x^2 = 720 \\ \Leftrightarrow x^2 = \frac{720}{5}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
6. \(-2x^2+72=0 \\ \Leftrightarrow -2x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-2}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
7. \(2(8x^2+10)=-(-15x^2-189) \\ \Leftrightarrow 16x^2+20=15x^2+189 \\ \Leftrightarrow 16x^2-15x^2=189-20 \\ \Leftrightarrow x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
8. \(3(10x^2+3)=-(-25x^2-29) \\ \Leftrightarrow 30x^2+9=25x^2+29 \\ \Leftrightarrow 30x^2-25x^2=29-9 \\ \Leftrightarrow 5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
9. \(-2(2x^2+6)=-(12x^2+660) \\ \Leftrightarrow -4x^2-12=-12x^2-660 \\ \Leftrightarrow -4x^2+12x^2=-660+12 \\ \Leftrightarrow 8x^2 = -648 \\ \Leftrightarrow x^2 = \frac{-648}{8} < 0 \\ V = \varnothing \\ -----------------\)
10. \(15x^2+964=7x^2-4 \\ \Leftrightarrow 15x^2-7x^2=-4-964 \\ \Leftrightarrow 8x^2 = -968 \\ \Leftrightarrow x^2 = \frac{-968}{8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-x^2+19=6x^2-9 \\ \Leftrightarrow -x^2-6x^2=-9-19 \\ \Leftrightarrow -7x^2 = -28 \\ \Leftrightarrow x^2 = \frac{-28}{-7}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(5(10x^2+8)=-(-48x^2-282) \\ \Leftrightarrow 50x^2+40=48x^2+282 \\ \Leftrightarrow 50x^2-48x^2=282-40 \\ \Leftrightarrow 2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)