Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(7x^2-232=9x^2+10\)
2. \(15x^2-286=7x^2+2\)
3. \(-2x^2-458=-9x^2-10\)
4. \(-11x^2-354=-8x^2+9\)
5. \(8x^2+179=9x^2+10\)
6. \(-3x^2-10=-2x^2-10\)
7. \(-11x^2+458=-4x^2+10\)
8. \(-5x^2+80=0\)
9. \(-5x^2+180=0\)
10. \(5x^2+0=0\)
11. \(-6x^2+384=0\)
12. \(x^2-1=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(7x^2-232=9x^2+10 \\ \Leftrightarrow 7x^2-9x^2=10+232 \\ \Leftrightarrow -2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{-2} < 0 \\ V = \varnothing \\ -----------------\)
2. \(15x^2-286=7x^2+2 \\ \Leftrightarrow 15x^2-7x^2=2+286 \\ \Leftrightarrow 8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
3. \(-2x^2-458=-9x^2-10 \\ \Leftrightarrow -2x^2+9x^2=-10+458 \\ \Leftrightarrow 7x^2 = 448 \\ \Leftrightarrow x^2 = \frac{448}{7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
4. \(-11x^2-354=-8x^2+9 \\ \Leftrightarrow -11x^2+8x^2=9+354 \\ \Leftrightarrow -3x^2 = 363 \\ \Leftrightarrow x^2 = \frac{363}{-3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(8x^2+179=9x^2+10 \\ \Leftrightarrow 8x^2-9x^2=10-179 \\ \Leftrightarrow -x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{-1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
6. \(-3x^2-10=-2x^2-10 \\ \Leftrightarrow -3x^2+2x^2=-10+10 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-11x^2+458=-4x^2+10 \\ \Leftrightarrow -11x^2+4x^2=10-458 \\ \Leftrightarrow -7x^2 = -448 \\ \Leftrightarrow x^2 = \frac{-448}{-7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
8. \(-5x^2+80=0 \\ \Leftrightarrow -5x^2 = -80 \\ \Leftrightarrow x^2 = \frac{-80}{-5}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
9. \(-5x^2+180=0 \\ \Leftrightarrow -5x^2 = -180 \\ \Leftrightarrow x^2 = \frac{-180}{-5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
10. \(5x^2+0=0 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-6x^2+384=0 \\ \Leftrightarrow -6x^2 = -384 \\ \Leftrightarrow x^2 = \frac{-384}{-6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
12. \(x^2-1=0 \\ \Leftrightarrow x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{1}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)