Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3x^2+192=0\)
2. \(-5x^2+980=0\)
3. \(-4(-4x^2+10)=-(-17x^2+209)\)
4. \(6x^2+9=9x^2+9\)
5. \(-11x^2+57=-7x^2-7\)
6. \(4(7x^2-7)=-(-29x^2+32)\)
7. \(2(-4x^2+10)=-(9x^2+205)\)
8. \(4(-9x^2-9)=-(30x^2+132)\)
9. \(-10x^2-898=-6x^2+2\)
10. \(-7x^2-63=0\)
11. \(15x^2-840=8x^2+7\)
12. \(-2x^2-75=3x^2+5\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3x^2+192=0 \\ \Leftrightarrow -3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{-3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
2. \(-5x^2+980=0 \\ \Leftrightarrow -5x^2 = -980 \\ \Leftrightarrow x^2 = \frac{-980}{-5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
3. \(-4(-4x^2+10)=-(-17x^2+209) \\ \Leftrightarrow 16x^2-40=17x^2-209 \\ \Leftrightarrow 16x^2-17x^2=-209+40 \\ \Leftrightarrow -x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{-1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
4. \(6x^2+9=9x^2+9 \\ \Leftrightarrow 6x^2-9x^2=9-9 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(-11x^2+57=-7x^2-7 \\ \Leftrightarrow -11x^2+7x^2=-7-57 \\ \Leftrightarrow -4x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
6. \(4(7x^2-7)=-(-29x^2+32) \\ \Leftrightarrow 28x^2-28=29x^2-32 \\ \Leftrightarrow 28x^2-29x^2=-32+28 \\ \Leftrightarrow -x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-1}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
7. \(2(-4x^2+10)=-(9x^2+205) \\ \Leftrightarrow -8x^2+20=-9x^2-205 \\ \Leftrightarrow -8x^2+9x^2=-205-20 \\ \Leftrightarrow x^2 = -225 \\ \Leftrightarrow x^2 = \frac{-225}{1} < 0 \\ V = \varnothing \\ -----------------\)
8. \(4(-9x^2-9)=-(30x^2+132) \\ \Leftrightarrow -36x^2-36=-30x^2-132 \\ \Leftrightarrow -36x^2+30x^2=-132+36 \\ \Leftrightarrow -6x^2 = -96 \\ \Leftrightarrow x^2 = \frac{-96}{-6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
9. \(-10x^2-898=-6x^2+2 \\ \Leftrightarrow -10x^2+6x^2=2+898 \\ \Leftrightarrow -4x^2 = 900 \\ \Leftrightarrow x^2 = \frac{900}{-4} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-7x^2-63=0 \\ \Leftrightarrow -7x^2 = 63 \\ \Leftrightarrow x^2 = \frac{63}{-7} < 0 \\ V = \varnothing \\ -----------------\)
11. \(15x^2-840=8x^2+7 \\ \Leftrightarrow 15x^2-8x^2=7+840 \\ \Leftrightarrow 7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
12. \(-2x^2-75=3x^2+5 \\ \Leftrightarrow -2x^2-3x^2=5+75 \\ \Leftrightarrow -5x^2 = 80 \\ \Leftrightarrow x^2 = \frac{80}{-5} < 0 \\ V = \varnothing \\ -----------------\)