Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(7x^2+7)=-(-22x^2-754)\)
2. \(4x^2-2=5x^2+7\)
3. \(6x^2-191=5x^2+5\)
4. \(6x^2+486=0\)
5. \(-7x^2-567=0\)
6. \(x^2+81=0\)
7. \(-9x^2+186=-8x^2-10\)
8. \(3(7x^2-8)=-(-19x^2+26)\)
9. \(4x^2-100=0\)
10. \(2(5x^2-2)=-(-3x^2-563)\)
11. \(x^2-143=4x^2+4\)
12. \(3(10x^2+8)=-(-34x^2-40)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(7x^2+7)=-(-22x^2-754) \\ \Leftrightarrow 28x^2+28=22x^2+754 \\ \Leftrightarrow 28x^2-22x^2=754-28 \\ \Leftrightarrow 6x^2 = 726 \\ \Leftrightarrow x^2 = \frac{726}{6}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
2. \(4x^2-2=5x^2+7 \\ \Leftrightarrow 4x^2-5x^2=7+2 \\ \Leftrightarrow -x^2 = 9 \\ \Leftrightarrow x^2 = \frac{9}{-1} < 0 \\ V = \varnothing \\ -----------------\)
3. \(6x^2-191=5x^2+5 \\ \Leftrightarrow 6x^2-5x^2=5+191 \\ \Leftrightarrow x^2 = 196 \\ \Leftrightarrow x^2 = \frac{196}{1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
4. \(6x^2+486=0 \\ \Leftrightarrow 6x^2 = -486 \\ \Leftrightarrow x^2 = \frac{-486}{6} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-7x^2-567=0 \\ \Leftrightarrow -7x^2 = 567 \\ \Leftrightarrow x^2 = \frac{567}{-7} < 0 \\ V = \varnothing \\ -----------------\)
6. \(x^2+81=0 \\ \Leftrightarrow x^2 = -81 \\ \Leftrightarrow x^2 = \frac{-81}{1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-9x^2+186=-8x^2-10 \\ \Leftrightarrow -9x^2+8x^2=-10-186 \\ \Leftrightarrow -x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
8. \(3(7x^2-8)=-(-19x^2+26) \\ \Leftrightarrow 21x^2-24=19x^2-26 \\ \Leftrightarrow 21x^2-19x^2=-26+24 \\ \Leftrightarrow 2x^2 = -2 \\ \Leftrightarrow x^2 = \frac{-2}{2} < 0 \\ V = \varnothing \\ -----------------\)
9. \(4x^2-100=0 \\ \Leftrightarrow 4x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{4}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(2(5x^2-2)=-(-3x^2-563) \\ \Leftrightarrow 10x^2-4=3x^2+563 \\ \Leftrightarrow 10x^2-3x^2=563+4 \\ \Leftrightarrow 7x^2 = 567 \\ \Leftrightarrow x^2 = \frac{567}{7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
11. \(x^2-143=4x^2+4 \\ \Leftrightarrow x^2-4x^2=4+143 \\ \Leftrightarrow -3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{-3} < 0 \\ V = \varnothing \\ -----------------\)
12. \(3(10x^2+8)=-(-34x^2-40) \\ \Leftrightarrow 30x^2+24=34x^2+40 \\ \Leftrightarrow 30x^2-34x^2=40-24 \\ \Leftrightarrow -4x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{-4} < 0 \\ V = \varnothing \\ -----------------\)