Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2-16=0\)
2. \(-2(2x^2-10)=-(x^2-167)\)
3. \(-15x^2-1146=-7x^2+6\)
4. \(-4(3x^2+7)=-(6x^2+1378)\)
5. \(-17x^2-134=-9x^2-6\)
6. \(7x^2-1575=0\)
7. \(2(10x^2-7)=-(-27x^2+1197)\)
8. \(-4x^2+36=0\)
9. \(-3x^2+675=0\)
10. \(-2x^2+2=-8x^2+2\)
11. \(x^2-247=-3x^2+9\)
12. \(-18x^2-63=-10x^2+9\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2-16=0 \\ \Leftrightarrow x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{1}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
2. \(-2(2x^2-10)=-(x^2-167) \\ \Leftrightarrow -4x^2+20=-x^2+167 \\ \Leftrightarrow -4x^2+x^2=167-20 \\ \Leftrightarrow -3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{-3} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-15x^2-1146=-7x^2+6 \\ \Leftrightarrow -15x^2+7x^2=6+1146 \\ \Leftrightarrow -8x^2 = 1152 \\ \Leftrightarrow x^2 = \frac{1152}{-8} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-4(3x^2+7)=-(6x^2+1378) \\ \Leftrightarrow -12x^2-28=-6x^2-1378 \\ \Leftrightarrow -12x^2+6x^2=-1378+28 \\ \Leftrightarrow -6x^2 = -1350 \\ \Leftrightarrow x^2 = \frac{-1350}{-6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
5. \(-17x^2-134=-9x^2-6 \\ \Leftrightarrow -17x^2+9x^2=-6+134 \\ \Leftrightarrow -8x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{-8} < 0 \\ V = \varnothing \\ -----------------\)
6. \(7x^2-1575=0 \\ \Leftrightarrow 7x^2 = 1575 \\ \Leftrightarrow x^2 = \frac{1575}{7}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
7. \(2(10x^2-7)=-(-27x^2+1197) \\ \Leftrightarrow 20x^2-14=27x^2-1197 \\ \Leftrightarrow 20x^2-27x^2=-1197+14 \\ \Leftrightarrow -7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
8. \(-4x^2+36=0 \\ \Leftrightarrow -4x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
9. \(-3x^2+675=0 \\ \Leftrightarrow -3x^2 = -675 \\ \Leftrightarrow x^2 = \frac{-675}{-3}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
10. \(-2x^2+2=-8x^2+2 \\ \Leftrightarrow -2x^2+8x^2=2-2 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(x^2-247=-3x^2+9 \\ \Leftrightarrow x^2+3x^2=9+247 \\ \Leftrightarrow 4x^2 = 256 \\ \Leftrightarrow x^2 = \frac{256}{4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
12. \(-18x^2-63=-10x^2+9 \\ \Leftrightarrow -18x^2+10x^2=9+63 \\ \Leftrightarrow -8x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{-8} < 0 \\ V = \varnothing \\ -----------------\)