Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(17x^2+390=9x^2-2\)
2. \(-4x^2+978=-9x^2-2\)
3. \(-x^2-102=-3x^2-4\)
4. \(5x^2-125=0\)
5. \(-x^2+81=0\)
6. \(-4x^2-100=0\)
7. \(x^2+331=3x^2-7\)
8. \(4x^2-400=0\)
9. \(7x^2-28=0\)
10. \(4(2x^2-7)=-(-2x^2-836)\)
11. \(3x^2-48=0\)
12. \(-2x^2-703=5x^2-3\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(17x^2+390=9x^2-2 \\ \Leftrightarrow 17x^2-9x^2=-2-390 \\ \Leftrightarrow 8x^2 = -392 \\ \Leftrightarrow x^2 = \frac{-392}{8} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-4x^2+978=-9x^2-2 \\ \Leftrightarrow -4x^2+9x^2=-2-978 \\ \Leftrightarrow 5x^2 = -980 \\ \Leftrightarrow x^2 = \frac{-980}{5} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-x^2-102=-3x^2-4 \\ \Leftrightarrow -x^2+3x^2=-4+102 \\ \Leftrightarrow 2x^2 = 98 \\ \Leftrightarrow x^2 = \frac{98}{2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
4. \(5x^2-125=0 \\ \Leftrightarrow 5x^2 = 125 \\ \Leftrightarrow x^2 = \frac{125}{5}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(-x^2+81=0 \\ \Leftrightarrow -x^2 = -81 \\ \Leftrightarrow x^2 = \frac{-81}{-1}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
6. \(-4x^2-100=0 \\ \Leftrightarrow -4x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{-4} < 0 \\ V = \varnothing \\ -----------------\)
7. \(x^2+331=3x^2-7 \\ \Leftrightarrow x^2-3x^2=-7-331 \\ \Leftrightarrow -2x^2 = -338 \\ \Leftrightarrow x^2 = \frac{-338}{-2}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
8. \(4x^2-400=0 \\ \Leftrightarrow 4x^2 = 400 \\ \Leftrightarrow x^2 = \frac{400}{4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
9. \(7x^2-28=0 \\ \Leftrightarrow 7x^2 = 28 \\ \Leftrightarrow x^2 = \frac{28}{7}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
10. \(4(2x^2-7)=-(-2x^2-836) \\ \Leftrightarrow 8x^2-28=2x^2+836 \\ \Leftrightarrow 8x^2-2x^2=836+28 \\ \Leftrightarrow 6x^2 = 864 \\ \Leftrightarrow x^2 = \frac{864}{6}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
11. \(3x^2-48=0 \\ \Leftrightarrow 3x^2 = 48 \\ \Leftrightarrow x^2 = \frac{48}{3}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
12. \(-2x^2-703=5x^2-3 \\ \Leftrightarrow -2x^2-5x^2=-3+703 \\ \Leftrightarrow -7x^2 = 700 \\ \Leftrightarrow x^2 = \frac{700}{-7} < 0 \\ V = \varnothing \\ -----------------\)