Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3(-7x^2-7)=-(15x^2+237)\)
2. \(-2x^2+98=0\)
3. \(-3(-7x^2-7)=-(-18x^2-48)\)
4. \(7x^2-343=0\)
5. \(2(-6x^2+2)=-(10x^2+4)\)
6. \(-9x^2+906=-5x^2+6\)
7. \(-2x^2+50=0\)
8. \(7x^2-847=0\)
9. \(-3(10x^2+6)=-(26x^2-178)\)
10. \(-2(4x^2-4)=-(14x^2+1006)\)
11. \(5x^2+0=0\)
12. \(7x^2+7=10x^2+7\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3(-7x^2-7)=-(15x^2+237) \\ \Leftrightarrow -21x^2-21=-15x^2-237 \\ \Leftrightarrow -21x^2+15x^2=-237+21 \\ \Leftrightarrow -6x^2 = -216 \\ \Leftrightarrow x^2 = \frac{-216}{-6}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
2. \(-2x^2+98=0 \\ \Leftrightarrow -2x^2 = -98 \\ \Leftrightarrow x^2 = \frac{-98}{-2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
3. \(-3(-7x^2-7)=-(-18x^2-48) \\ \Leftrightarrow 21x^2+21=18x^2+48 \\ \Leftrightarrow 21x^2-18x^2=48-21 \\ \Leftrightarrow 3x^2 = 27 \\ \Leftrightarrow x^2 = \frac{27}{3}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
4. \(7x^2-343=0 \\ \Leftrightarrow 7x^2 = 343 \\ \Leftrightarrow x^2 = \frac{343}{7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
5. \(2(-6x^2+2)=-(10x^2+4) \\ \Leftrightarrow -12x^2+4=-10x^2-4 \\ \Leftrightarrow -12x^2+10x^2=-4-4 \\ \Leftrightarrow -2x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
6. \(-9x^2+906=-5x^2+6 \\ \Leftrightarrow -9x^2+5x^2=6-906 \\ \Leftrightarrow -4x^2 = -900 \\ \Leftrightarrow x^2 = \frac{-900}{-4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
7. \(-2x^2+50=0 \\ \Leftrightarrow -2x^2 = -50 \\ \Leftrightarrow x^2 = \frac{-50}{-2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
8. \(7x^2-847=0 \\ \Leftrightarrow 7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(-3(10x^2+6)=-(26x^2-178) \\ \Leftrightarrow -30x^2-18=-26x^2+178 \\ \Leftrightarrow -30x^2+26x^2=178+18 \\ \Leftrightarrow -4x^2 = 196 \\ \Leftrightarrow x^2 = \frac{196}{-4} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-2(4x^2-4)=-(14x^2+1006) \\ \Leftrightarrow -8x^2+8=-14x^2-1006 \\ \Leftrightarrow -8x^2+14x^2=-1006-8 \\ \Leftrightarrow 6x^2 = -1014 \\ \Leftrightarrow x^2 = \frac{-1014}{6} < 0 \\ V = \varnothing \\ -----------------\)
11. \(5x^2+0=0 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(7x^2+7=10x^2+7 \\ \Leftrightarrow 7x^2-10x^2=7-7 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)