Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(9x^2+2)=-(41x^2+586)\)
2. \(-2x^2-8=0\)
3. \(2(3x^2+6)=-(-x^2+233)\)
4. \(3x^2+588=0\)
5. \(-7x^2+1183=0\)
6. \(5(-3x^2+8)=-(21x^2-904)\)
7. \(-3x^2+70=2x^2-10\)
8. \(6x^2+486=0\)
9. \(3(-2x^2+9)=-(9x^2-174)\)
10. \(-5x^2+0=0\)
11. \(5x^2+23=-2x^2-5\)
12. \(8x^2+8=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(9x^2+2)=-(41x^2+586) \\ \Leftrightarrow -45x^2-10=-41x^2-586 \\ \Leftrightarrow -45x^2+41x^2=-586+10 \\ \Leftrightarrow -4x^2 = -576 \\ \Leftrightarrow x^2 = \frac{-576}{-4}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
2. \(-2x^2-8=0 \\ \Leftrightarrow -2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{-2} < 0 \\ V = \varnothing \\ -----------------\)
3. \(2(3x^2+6)=-(-x^2+233) \\ \Leftrightarrow 6x^2+12=x^2-233 \\ \Leftrightarrow 6x^2-x^2=-233-12 \\ \Leftrightarrow 5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{5} < 0 \\ V = \varnothing \\ -----------------\)
4. \(3x^2+588=0 \\ \Leftrightarrow 3x^2 = -588 \\ \Leftrightarrow x^2 = \frac{-588}{3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-7x^2+1183=0 \\ \Leftrightarrow -7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
6. \(5(-3x^2+8)=-(21x^2-904) \\ \Leftrightarrow -15x^2+40=-21x^2+904 \\ \Leftrightarrow -15x^2+21x^2=904-40 \\ \Leftrightarrow 6x^2 = 864 \\ \Leftrightarrow x^2 = \frac{864}{6}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
7. \(-3x^2+70=2x^2-10 \\ \Leftrightarrow -3x^2-2x^2=-10-70 \\ \Leftrightarrow -5x^2 = -80 \\ \Leftrightarrow x^2 = \frac{-80}{-5}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
8. \(6x^2+486=0 \\ \Leftrightarrow 6x^2 = -486 \\ \Leftrightarrow x^2 = \frac{-486}{6} < 0 \\ V = \varnothing \\ -----------------\)
9. \(3(-2x^2+9)=-(9x^2-174) \\ \Leftrightarrow -6x^2+27=-9x^2+174 \\ \Leftrightarrow -6x^2+9x^2=174-27 \\ \Leftrightarrow 3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{3}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
10. \(-5x^2+0=0 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(5x^2+23=-2x^2-5 \\ \Leftrightarrow 5x^2+2x^2=-5-23 \\ \Leftrightarrow 7x^2 = -28 \\ \Leftrightarrow x^2 = \frac{-28}{7} < 0 \\ V = \varnothing \\ -----------------\)
12. \(8x^2+8=0 \\ \Leftrightarrow 8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{8} < 0 \\ V = \varnothing \\ -----------------\)