Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-11x^2+1017=-5x^2+3\)
2. \(6x^2+6=10x^2-10\)
3. \(3x^2-507=0\)
4. \(-5x^2+80=0\)
5. \(-5x^2+361=-8x^2-2\)
6. \(-x^2+64=0\)
7. \(4x^2+576=0\)
8. \(-8x^2+128=0\)
9. \(5(-10x^2+5)=-(47x^2+50)\)
10. \(5x^2+720=0\)
11. \(4(6x^2+4)=-(-25x^2+153)\)
12. \(-x^2-8=5x^2-8\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-11x^2+1017=-5x^2+3 \\ \Leftrightarrow -11x^2+5x^2=3-1017 \\ \Leftrightarrow -6x^2 = -1014 \\ \Leftrightarrow x^2 = \frac{-1014}{-6}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
2. \(6x^2+6=10x^2-10 \\ \Leftrightarrow 6x^2-10x^2=-10-6 \\ \Leftrightarrow -4x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{-4}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
3. \(3x^2-507=0 \\ \Leftrightarrow 3x^2 = 507 \\ \Leftrightarrow x^2 = \frac{507}{3}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
4. \(-5x^2+80=0 \\ \Leftrightarrow -5x^2 = -80 \\ \Leftrightarrow x^2 = \frac{-80}{-5}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
5. \(-5x^2+361=-8x^2-2 \\ \Leftrightarrow -5x^2+8x^2=-2-361 \\ \Leftrightarrow 3x^2 = -363 \\ \Leftrightarrow x^2 = \frac{-363}{3} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-x^2+64=0 \\ \Leftrightarrow -x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-1}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
7. \(4x^2+576=0 \\ \Leftrightarrow 4x^2 = -576 \\ \Leftrightarrow x^2 = \frac{-576}{4} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-8x^2+128=0 \\ \Leftrightarrow -8x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-8}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
9. \(5(-10x^2+5)=-(47x^2+50) \\ \Leftrightarrow -50x^2+25=-47x^2-50 \\ \Leftrightarrow -50x^2+47x^2=-50-25 \\ \Leftrightarrow -3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{-3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(5x^2+720=0 \\ \Leftrightarrow 5x^2 = -720 \\ \Leftrightarrow x^2 = \frac{-720}{5} < 0 \\ V = \varnothing \\ -----------------\)
11. \(4(6x^2+4)=-(-25x^2+153) \\ \Leftrightarrow 24x^2+16=25x^2-153 \\ \Leftrightarrow 24x^2-25x^2=-153-16 \\ \Leftrightarrow -x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{-1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
12. \(-x^2-8=5x^2-8 \\ \Leftrightarrow -x^2-5x^2=-8+8 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)