Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2x^2-200=0\)
2. \(-5(4x^2-5)=-(26x^2+29)\)
3. \(10x^2-58=3x^2+5\)
4. \(7x^2-607=2x^2-2\)
5. \(-7x^2-255=-2x^2-10\)
6. \(3(-7x^2-8)=-(20x^2+49)\)
7. \(-2(5x^2+8)=-(17x^2-96)\)
8. \(-8x^2+6=-3x^2+6\)
9. \(4x^2-774=8x^2+10\)
10. \(-8x^2+1568=0\)
11. \(2(7x^2+6)=-(-22x^2+1340)\)
12. \(-6x^2+2=2x^2+2\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2x^2-200=0 \\ \Leftrightarrow 2x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{2}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
2. \(-5(4x^2-5)=-(26x^2+29) \\ \Leftrightarrow -20x^2+25=-26x^2-29 \\ \Leftrightarrow -20x^2+26x^2=-29-25 \\ \Leftrightarrow 6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{6} < 0 \\ V = \varnothing \\ -----------------\)
3. \(10x^2-58=3x^2+5 \\ \Leftrightarrow 10x^2-3x^2=5+58 \\ \Leftrightarrow 7x^2 = 63 \\ \Leftrightarrow x^2 = \frac{63}{7}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
4. \(7x^2-607=2x^2-2 \\ \Leftrightarrow 7x^2-2x^2=-2+607 \\ \Leftrightarrow 5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
5. \(-7x^2-255=-2x^2-10 \\ \Leftrightarrow -7x^2+2x^2=-10+255 \\ \Leftrightarrow -5x^2 = 245 \\ \Leftrightarrow x^2 = \frac{245}{-5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(3(-7x^2-8)=-(20x^2+49) \\ \Leftrightarrow -21x^2-24=-20x^2-49 \\ \Leftrightarrow -21x^2+20x^2=-49+24 \\ \Leftrightarrow -x^2 = -25 \\ \Leftrightarrow x^2 = \frac{-25}{-1}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
7. \(-2(5x^2+8)=-(17x^2-96) \\ \Leftrightarrow -10x^2-16=-17x^2+96 \\ \Leftrightarrow -10x^2+17x^2=96+16 \\ \Leftrightarrow 7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
8. \(-8x^2+6=-3x^2+6 \\ \Leftrightarrow -8x^2+3x^2=6-6 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(4x^2-774=8x^2+10 \\ \Leftrightarrow 4x^2-8x^2=10+774 \\ \Leftrightarrow -4x^2 = 784 \\ \Leftrightarrow x^2 = \frac{784}{-4} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-8x^2+1568=0 \\ \Leftrightarrow -8x^2 = -1568 \\ \Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
11. \(2(7x^2+6)=-(-22x^2+1340) \\ \Leftrightarrow 14x^2+12=22x^2-1340 \\ \Leftrightarrow 14x^2-22x^2=-1340-12 \\ \Leftrightarrow -8x^2 = -1352 \\ \Leftrightarrow x^2 = \frac{-1352}{-8}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
12. \(-6x^2+2=2x^2+2 \\ \Leftrightarrow -6x^2-2x^2=2-2 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)