Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(17x^2-851=10x^2-4\)
2. \(-x^2+7=-6x^2+7\)
3. \(-8x^2-288=0\)
4. \(-5x^2-845=0\)
5. \(-3x^2+507=0\)
6. \(-3(-9x^2+9)=-(-20x^2+1210)\)
7. \(-3x^2+9=-5x^2-9\)
8. \(-6x^2-33=-7x^2-8\)
9. \(3x^2-675=0\)
10. \(2x^2-338=0\)
11. \(2x^2-72=0\)
12. \(-2x^2-18=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(17x^2-851=10x^2-4 \\ \Leftrightarrow 17x^2-10x^2=-4+851 \\ \Leftrightarrow 7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
2. \(-x^2+7=-6x^2+7 \\ \Leftrightarrow -x^2+6x^2=7-7 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-8x^2-288=0 \\ \Leftrightarrow -8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{-8} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-5x^2-845=0 \\ \Leftrightarrow -5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{-5} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-3x^2+507=0 \\ \Leftrightarrow -3x^2 = -507 \\ \Leftrightarrow x^2 = \frac{-507}{-3}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
6. \(-3(-9x^2+9)=-(-20x^2+1210) \\ \Leftrightarrow 27x^2-27=20x^2-1210 \\ \Leftrightarrow 27x^2-20x^2=-1210+27 \\ \Leftrightarrow 7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{7} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-3x^2+9=-5x^2-9 \\ \Leftrightarrow -3x^2+5x^2=-9-9 \\ \Leftrightarrow 2x^2 = -18 \\ \Leftrightarrow x^2 = \frac{-18}{2} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-6x^2-33=-7x^2-8 \\ \Leftrightarrow -6x^2+7x^2=-8+33 \\ \Leftrightarrow x^2 = 25 \\ \Leftrightarrow x^2 = \frac{25}{1}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
9. \(3x^2-675=0 \\ \Leftrightarrow 3x^2 = 675 \\ \Leftrightarrow x^2 = \frac{675}{3}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
10. \(2x^2-338=0 \\ \Leftrightarrow 2x^2 = 338 \\ \Leftrightarrow x^2 = \frac{338}{2}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
11. \(2x^2-72=0 \\ \Leftrightarrow 2x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{2}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
12. \(-2x^2-18=0 \\ \Leftrightarrow -2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{-2} < 0 \\ V = \varnothing \\ -----------------\)