Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(9x^2-10)=-(-20x^2-108)\)
2. \(7x^2+175=0\)
3. \(2x^2+902=6x^2+2\)
4. \(-13x^2-1=-7x^2-7\)
5. \(-4(7x^2+2)=-(20x^2+208)\)
6. \(2x^2-493=-2x^2-9\)
7. \(-7x^2-6=-8x^2-10\)
8. \(-x^2-21=6x^2+7\)
9. \(5x^2-605=0\)
10. \(4(-4x^2-3)=-(21x^2+192)\)
11. \(8x^2+8=0\)
12. \(-4x^2+144=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(9x^2-10)=-(-20x^2-108) \\ \Leftrightarrow 18x^2-20=20x^2+108 \\ \Leftrightarrow 18x^2-20x^2=108+20 \\ \Leftrightarrow -2x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{-2} < 0 \\ V = \varnothing \\ -----------------\)
2. \(7x^2+175=0 \\ \Leftrightarrow 7x^2 = -175 \\ \Leftrightarrow x^2 = \frac{-175}{7} < 0 \\ V = \varnothing \\ -----------------\)
3. \(2x^2+902=6x^2+2 \\ \Leftrightarrow 2x^2-6x^2=2-902 \\ \Leftrightarrow -4x^2 = -900 \\ \Leftrightarrow x^2 = \frac{-900}{-4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
4. \(-13x^2-1=-7x^2-7 \\ \Leftrightarrow -13x^2+7x^2=-7+1 \\ \Leftrightarrow -6x^2 = -6 \\ \Leftrightarrow x^2 = \frac{-6}{-6}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
5. \(-4(7x^2+2)=-(20x^2+208) \\ \Leftrightarrow -28x^2-8=-20x^2-208 \\ \Leftrightarrow -28x^2+20x^2=-208+8 \\ \Leftrightarrow -8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
6. \(2x^2-493=-2x^2-9 \\ \Leftrightarrow 2x^2+2x^2=-9+493 \\ \Leftrightarrow 4x^2 = 484 \\ \Leftrightarrow x^2 = \frac{484}{4}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
7. \(-7x^2-6=-8x^2-10 \\ \Leftrightarrow -7x^2+8x^2=-10+6 \\ \Leftrightarrow x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{1} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-x^2-21=6x^2+7 \\ \Leftrightarrow -x^2-6x^2=7+21 \\ \Leftrightarrow -7x^2 = 28 \\ \Leftrightarrow x^2 = \frac{28}{-7} < 0 \\ V = \varnothing \\ -----------------\)
9. \(5x^2-605=0 \\ \Leftrightarrow 5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
10. \(4(-4x^2-3)=-(21x^2+192) \\ \Leftrightarrow -16x^2-12=-21x^2-192 \\ \Leftrightarrow -16x^2+21x^2=-192+12 \\ \Leftrightarrow 5x^2 = -180 \\ \Leftrightarrow x^2 = \frac{-180}{5} < 0 \\ V = \varnothing \\ -----------------\)
11. \(8x^2+8=0 \\ \Leftrightarrow 8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{8} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-4x^2+144=0 \\ \Leftrightarrow -4x^2 = -144 \\ \Leftrightarrow x^2 = \frac{-144}{-4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)