Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3x^2+9=4x^2+9\)
2. \(-2(-7x^2-9)=-(-22x^2+950)\)
3. \(8x^2-7=2x^2-7\)
4. \(x^2-963=-7x^2+5\)
5. \(-2x^2-12=3x^2-7\)
6. \(-5(9x^2-10)=-(40x^2+555)\)
7. \(5x^2-62=4x^2+2\)
8. \(-4x^2-299=-10x^2-5\)
9. \(-4(8x^2-10)=-(39x^2+303)\)
10. \(2x^2-162=0\)
11. \(6x^2-150=0\)
12. \(x^2-489=7x^2-3\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3x^2+9=4x^2+9 \\ \Leftrightarrow -3x^2-4x^2=9-9 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-2(-7x^2-9)=-(-22x^2+950) \\ \Leftrightarrow 14x^2+18=22x^2-950 \\ \Leftrightarrow 14x^2-22x^2=-950-18 \\ \Leftrightarrow -8x^2 = -968 \\ \Leftrightarrow x^2 = \frac{-968}{-8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
3. \(8x^2-7=2x^2-7 \\ \Leftrightarrow 8x^2-2x^2=-7+7 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(x^2-963=-7x^2+5 \\ \Leftrightarrow x^2+7x^2=5+963 \\ \Leftrightarrow 8x^2 = 968 \\ \Leftrightarrow x^2 = \frac{968}{8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
5. \(-2x^2-12=3x^2-7 \\ \Leftrightarrow -2x^2-3x^2=-7+12 \\ \Leftrightarrow -5x^2 = 5 \\ \Leftrightarrow x^2 = \frac{5}{-5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-5(9x^2-10)=-(40x^2+555) \\ \Leftrightarrow -45x^2+50=-40x^2-555 \\ \Leftrightarrow -45x^2+40x^2=-555-50 \\ \Leftrightarrow -5x^2 = -605 \\ \Leftrightarrow x^2 = \frac{-605}{-5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
7. \(5x^2-62=4x^2+2 \\ \Leftrightarrow 5x^2-4x^2=2+62 \\ \Leftrightarrow x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{1}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
8. \(-4x^2-299=-10x^2-5 \\ \Leftrightarrow -4x^2+10x^2=-5+299 \\ \Leftrightarrow 6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
9. \(-4(8x^2-10)=-(39x^2+303) \\ \Leftrightarrow -32x^2+40=-39x^2-303 \\ \Leftrightarrow -32x^2+39x^2=-303-40 \\ \Leftrightarrow 7x^2 = -343 \\ \Leftrightarrow x^2 = \frac{-343}{7} < 0 \\ V = \varnothing \\ -----------------\)
10. \(2x^2-162=0 \\ \Leftrightarrow 2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
11. \(6x^2-150=0 \\ \Leftrightarrow 6x^2 = 150 \\ \Leftrightarrow x^2 = \frac{150}{6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
12. \(x^2-489=7x^2-3 \\ \Leftrightarrow x^2-7x^2=-3+489 \\ \Leftrightarrow -6x^2 = 486 \\ \Leftrightarrow x^2 = \frac{486}{-6} < 0 \\ V = \varnothing \\ -----------------\)