Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(-5x^2-3)=-(-19x^2-9)\)
2. \(9x^2+97=8x^2-3\)
3. \(16x^2+185=9x^2+10\)
4. \(-2x^2+236=3x^2-9\)
5. \(-3x^2+75=0\)
6. \(-8x^2+1352=0\)
7. \(-6x^2-726=0\)
8. \(5(-8x^2+3)=-(43x^2-90)\)
9. \(8x^2-151=7x^2-7\)
10. \(-3(2x^2-5)=-(14x^2+1337)\)
11. \(-4(10x^2+5)=-(34x^2-994)\)
12. \(3(-6x^2+7)=-(25x^2+546)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(-5x^2-3)=-(-19x^2-9) \\ \Leftrightarrow 25x^2+15=19x^2+9 \\ \Leftrightarrow 25x^2-19x^2=9-15 \\ \Leftrightarrow 6x^2 = -6 \\ \Leftrightarrow x^2 = \frac{-6}{6} < 0 \\ V = \varnothing \\ -----------------\)
2. \(9x^2+97=8x^2-3 \\ \Leftrightarrow 9x^2-8x^2=-3-97 \\ \Leftrightarrow x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{1} < 0 \\ V = \varnothing \\ -----------------\)
3. \(16x^2+185=9x^2+10 \\ \Leftrightarrow 16x^2-9x^2=10-185 \\ \Leftrightarrow 7x^2 = -175 \\ \Leftrightarrow x^2 = \frac{-175}{7} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-2x^2+236=3x^2-9 \\ \Leftrightarrow -2x^2-3x^2=-9-236 \\ \Leftrightarrow -5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{-5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
5. \(-3x^2+75=0 \\ \Leftrightarrow -3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{-3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
6. \(-8x^2+1352=0 \\ \Leftrightarrow -8x^2 = -1352 \\ \Leftrightarrow x^2 = \frac{-1352}{-8}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
7. \(-6x^2-726=0 \\ \Leftrightarrow -6x^2 = 726 \\ \Leftrightarrow x^2 = \frac{726}{-6} < 0 \\ V = \varnothing \\ -----------------\)
8. \(5(-8x^2+3)=-(43x^2-90) \\ \Leftrightarrow -40x^2+15=-43x^2+90 \\ \Leftrightarrow -40x^2+43x^2=90-15 \\ \Leftrightarrow 3x^2 = 75 \\ \Leftrightarrow x^2 = \frac{75}{3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
9. \(8x^2-151=7x^2-7 \\ \Leftrightarrow 8x^2-7x^2=-7+151 \\ \Leftrightarrow x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{1}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
10. \(-3(2x^2-5)=-(14x^2+1337) \\ \Leftrightarrow -6x^2+15=-14x^2-1337 \\ \Leftrightarrow -6x^2+14x^2=-1337-15 \\ \Leftrightarrow 8x^2 = -1352 \\ \Leftrightarrow x^2 = \frac{-1352}{8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-4(10x^2+5)=-(34x^2-994) \\ \Leftrightarrow -40x^2-20=-34x^2+994 \\ \Leftrightarrow -40x^2+34x^2=994+20 \\ \Leftrightarrow -6x^2 = 1014 \\ \Leftrightarrow x^2 = \frac{1014}{-6} < 0 \\ V = \varnothing \\ -----------------\)
12. \(3(-6x^2+7)=-(25x^2+546) \\ \Leftrightarrow -18x^2+21=-25x^2-546 \\ \Leftrightarrow -18x^2+25x^2=-546-21 \\ \Leftrightarrow 7x^2 = -567 \\ \Leftrightarrow x^2 = \frac{-567}{7} < 0 \\ V = \varnothing \\ -----------------\)