Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2-196=0\)
2. \(3(10x^2+10)=-(-33x^2+402)\)
3. \(5x^2+320=0\)
4. \(8x^2+1800=0\)
5. \(-4(9x^2-9)=-(29x^2+1336)\)
6. \(-4x^2+324=0\)
7. \(7x^2+0=0\)
8. \(-3x^2-432=0\)
9. \(5x^2-297=2x^2+3\)
10. \(4(-10x^2-10)=-(48x^2-160)\)
11. \(x^2-121=0\)
12. \(4(-4x^2-7)=-(21x^2+28)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2-196=0 \\ \Leftrightarrow x^2 = 196 \\ \Leftrightarrow x^2 = \frac{196}{1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
2. \(3(10x^2+10)=-(-33x^2+402) \\ \Leftrightarrow 30x^2+30=33x^2-402 \\ \Leftrightarrow 30x^2-33x^2=-402-30 \\ \Leftrightarrow -3x^2 = -432 \\ \Leftrightarrow x^2 = \frac{-432}{-3}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
3. \(5x^2+320=0 \\ \Leftrightarrow 5x^2 = -320 \\ \Leftrightarrow x^2 = \frac{-320}{5} < 0 \\ V = \varnothing \\ -----------------\)
4. \(8x^2+1800=0 \\ \Leftrightarrow 8x^2 = -1800 \\ \Leftrightarrow x^2 = \frac{-1800}{8} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-4(9x^2-9)=-(29x^2+1336) \\ \Leftrightarrow -36x^2+36=-29x^2-1336 \\ \Leftrightarrow -36x^2+29x^2=-1336-36 \\ \Leftrightarrow -7x^2 = -1372 \\ \Leftrightarrow x^2 = \frac{-1372}{-7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
6. \(-4x^2+324=0 \\ \Leftrightarrow -4x^2 = -324 \\ \Leftrightarrow x^2 = \frac{-324}{-4}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
7. \(7x^2+0=0 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(-3x^2-432=0 \\ \Leftrightarrow -3x^2 = 432 \\ \Leftrightarrow x^2 = \frac{432}{-3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(5x^2-297=2x^2+3 \\ \Leftrightarrow 5x^2-2x^2=3+297 \\ \Leftrightarrow 3x^2 = 300 \\ \Leftrightarrow x^2 = \frac{300}{3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
10. \(4(-10x^2-10)=-(48x^2-160) \\ \Leftrightarrow -40x^2-40=-48x^2+160 \\ \Leftrightarrow -40x^2+48x^2=160+40 \\ \Leftrightarrow 8x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
11. \(x^2-121=0 \\ \Leftrightarrow x^2 = 121 \\ \Leftrightarrow x^2 = \frac{121}{1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
12. \(4(-4x^2-7)=-(21x^2+28) \\ \Leftrightarrow -16x^2-28=-21x^2-28 \\ \Leftrightarrow -16x^2+21x^2=-28+28 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)