Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(11x^2+194=8x^2+2\)
2. \(-13x^2+774=-9x^2-10\)
3. \(-5x^2+970=3x^2+2\)
4. \(6x^2-486=0\)
5. \(8x^2+9=6x^2+9\)
6. \(5(5x^2+7)=-(-23x^2+37)\)
7. \(8x^2-288=0\)
8. \(8x^2+69=5x^2-6\)
9. \(5x^2-605=0\)
10. \(-4(2x^2+5)=-(11x^2+32)\)
11. \(7x^2-1008=0\)
12. \(-8x^2+1568=0\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(11x^2+194=8x^2+2 \\ \Leftrightarrow 11x^2-8x^2=2-194 \\ \Leftrightarrow 3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{3} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-13x^2+774=-9x^2-10 \\ \Leftrightarrow -13x^2+9x^2=-10-774 \\ \Leftrightarrow -4x^2 = -784 \\ \Leftrightarrow x^2 = \frac{-784}{-4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
3. \(-5x^2+970=3x^2+2 \\ \Leftrightarrow -5x^2-3x^2=2-970 \\ \Leftrightarrow -8x^2 = -968 \\ \Leftrightarrow x^2 = \frac{-968}{-8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
4. \(6x^2-486=0 \\ \Leftrightarrow 6x^2 = 486 \\ \Leftrightarrow x^2 = \frac{486}{6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
5. \(8x^2+9=6x^2+9 \\ \Leftrightarrow 8x^2-6x^2=9-9 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(5(5x^2+7)=-(-23x^2+37) \\ \Leftrightarrow 25x^2+35=23x^2-37 \\ \Leftrightarrow 25x^2-23x^2=-37-35 \\ \Leftrightarrow 2x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{2} < 0 \\ V = \varnothing \\ -----------------\)
7. \(8x^2-288=0 \\ \Leftrightarrow 8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
8. \(8x^2+69=5x^2-6 \\ \Leftrightarrow 8x^2-5x^2=-6-69 \\ \Leftrightarrow 3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(5x^2-605=0 \\ \Leftrightarrow 5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
10. \(-4(2x^2+5)=-(11x^2+32) \\ \Leftrightarrow -8x^2-20=-11x^2-32 \\ \Leftrightarrow -8x^2+11x^2=-32+20 \\ \Leftrightarrow 3x^2 = -12 \\ \Leftrightarrow x^2 = \frac{-12}{3} < 0 \\ V = \varnothing \\ -----------------\)
11. \(7x^2-1008=0 \\ \Leftrightarrow 7x^2 = 1008 \\ \Leftrightarrow x^2 = \frac{1008}{7}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
12. \(-8x^2+1568=0 \\ \Leftrightarrow -8x^2 = -1568 \\ \Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)