Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(7x^2+202=6x^2+6\)
2. \(3x^2-12=0\)
3. \(-11x^2+594=-8x^2+6\)
4. \(2(-2x^2+6)=-(x^2+231)\)
5. \(5x^2+605=0\)
6. \(-7x^2+1372=0\)
7. \(-2x^2-4=-8x^2-4\)
8. \(2(-8x^2+6)=-(18x^2+6)\)
9. \(4(9x^2-9)=-(-38x^2-206)\)
10. \(5x^2-500=0\)
11. \(2x^2-98=0\)
12. \(-3x^2+192=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(7x^2+202=6x^2+6 \\ \Leftrightarrow 7x^2-6x^2=6-202 \\ \Leftrightarrow x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(3x^2-12=0 \\ \Leftrightarrow 3x^2 = 12 \\ \Leftrightarrow x^2 = \frac{12}{3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
3. \(-11x^2+594=-8x^2+6 \\ \Leftrightarrow -11x^2+8x^2=6-594 \\ \Leftrightarrow -3x^2 = -588 \\ \Leftrightarrow x^2 = \frac{-588}{-3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
4. \(2(-2x^2+6)=-(x^2+231) \\ \Leftrightarrow -4x^2+12=-x^2-231 \\ \Leftrightarrow -4x^2+x^2=-231-12 \\ \Leftrightarrow -3x^2 = -243 \\ \Leftrightarrow x^2 = \frac{-243}{-3}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
5. \(5x^2+605=0 \\ \Leftrightarrow 5x^2 = -605 \\ \Leftrightarrow x^2 = \frac{-605}{5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-7x^2+1372=0 \\ \Leftrightarrow -7x^2 = -1372 \\ \Leftrightarrow x^2 = \frac{-1372}{-7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
7. \(-2x^2-4=-8x^2-4 \\ \Leftrightarrow -2x^2+8x^2=-4+4 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(2(-8x^2+6)=-(18x^2+6) \\ \Leftrightarrow -16x^2+12=-18x^2-6 \\ \Leftrightarrow -16x^2+18x^2=-6-12 \\ \Leftrightarrow 2x^2 = -18 \\ \Leftrightarrow x^2 = \frac{-18}{2} < 0 \\ V = \varnothing \\ -----------------\)
9. \(4(9x^2-9)=-(-38x^2-206) \\ \Leftrightarrow 36x^2-36=38x^2+206 \\ \Leftrightarrow 36x^2-38x^2=206+36 \\ \Leftrightarrow -2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{-2} < 0 \\ V = \varnothing \\ -----------------\)
10. \(5x^2-500=0 \\ \Leftrightarrow 5x^2 = 500 \\ \Leftrightarrow x^2 = \frac{500}{5}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
11. \(2x^2-98=0 \\ \Leftrightarrow 2x^2 = 98 \\ \Leftrightarrow x^2 = \frac{98}{2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
12. \(-3x^2+192=0 \\ \Leftrightarrow -3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{-3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)