Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(-7x^2+4)=-(-32x^2+20)\)
2. \(-5(10x^2+5)=-(58x^2+25)\)
3. \(-x^2+396=4x^2-9\)
4. \(x^2+25=0\)
5. \(4x^2+576=0\)
6. \(-2x^2-3=-8x^2-3\)
7. \(-3x^2-33=4x^2-5\)
8. \(3(-2x^2+4)=-(-2x^2+1140)\)
9. \(5(-3x^2+8)=-(8x^2-103)\)
10. \(6x^2-1176=0\)
11. \(x^2+90=3x^2-8\)
12. \(3x^2-517=-5x^2-5\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(-7x^2+4)=-(-32x^2+20) \\ \Leftrightarrow 35x^2-20=32x^2-20 \\ \Leftrightarrow 35x^2-32x^2=-20+20 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-5(10x^2+5)=-(58x^2+25) \\ \Leftrightarrow -50x^2-25=-58x^2-25 \\ \Leftrightarrow -50x^2+58x^2=-25+25 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-x^2+396=4x^2-9 \\ \Leftrightarrow -x^2-4x^2=-9-396 \\ \Leftrightarrow -5x^2 = -405 \\ \Leftrightarrow x^2 = \frac{-405}{-5}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
4. \(x^2+25=0 \\ \Leftrightarrow x^2 = -25 \\ \Leftrightarrow x^2 = \frac{-25}{1} < 0 \\ V = \varnothing \\ -----------------\)
5. \(4x^2+576=0 \\ \Leftrightarrow 4x^2 = -576 \\ \Leftrightarrow x^2 = \frac{-576}{4} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-2x^2-3=-8x^2-3 \\ \Leftrightarrow -2x^2+8x^2=-3+3 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-3x^2-33=4x^2-5 \\ \Leftrightarrow -3x^2-4x^2=-5+33 \\ \Leftrightarrow -7x^2 = 28 \\ \Leftrightarrow x^2 = \frac{28}{-7} < 0 \\ V = \varnothing \\ -----------------\)
8. \(3(-2x^2+4)=-(-2x^2+1140) \\ \Leftrightarrow -6x^2+12=2x^2-1140 \\ \Leftrightarrow -6x^2-2x^2=-1140-12 \\ \Leftrightarrow -8x^2 = -1152 \\ \Leftrightarrow x^2 = \frac{-1152}{-8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
9. \(5(-3x^2+8)=-(8x^2-103) \\ \Leftrightarrow -15x^2+40=-8x^2+103 \\ \Leftrightarrow -15x^2+8x^2=103-40 \\ \Leftrightarrow -7x^2 = 63 \\ \Leftrightarrow x^2 = \frac{63}{-7} < 0 \\ V = \varnothing \\ -----------------\)
10. \(6x^2-1176=0 \\ \Leftrightarrow 6x^2 = 1176 \\ \Leftrightarrow x^2 = \frac{1176}{6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
11. \(x^2+90=3x^2-8 \\ \Leftrightarrow x^2-3x^2=-8-90 \\ \Leftrightarrow -2x^2 = -98 \\ \Leftrightarrow x^2 = \frac{-98}{-2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
12. \(3x^2-517=-5x^2-5 \\ \Leftrightarrow 3x^2+5x^2=-5+517 \\ \Leftrightarrow 8x^2 = 512 \\ \Leftrightarrow x^2 = \frac{512}{8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)