Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2+11=-5x^2+2\)
2. \(-5x^2-7=-9x^2-7\)
3. \(2(-5x^2+9)=-(17x^2+1354)\)
4. \(-10x^2+347=-8x^2+9\)
5. \(8x^2-1346=2x^2+4\)
6. \(2(-5x^2-9)=-(3x^2+18)\)
7. \(-6x^2+201=-2x^2+5\)
8. \(7x^2-7=0\)
9. \(-3(-3x^2-10)=-(-11x^2-158)\)
10. \(-6x^2-69=-10x^2-5\)
11. \(-11x^2+38=-4x^2+10\)
12. \(5x^2+709=-2x^2+9\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2+11=-5x^2+2 \\ \Leftrightarrow -6x^2+5x^2=2-11 \\ \Leftrightarrow -x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{-1}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
2. \(-5x^2-7=-9x^2-7 \\ \Leftrightarrow -5x^2+9x^2=-7+7 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(2(-5x^2+9)=-(17x^2+1354) \\ \Leftrightarrow -10x^2+18=-17x^2-1354 \\ \Leftrightarrow -10x^2+17x^2=-1354-18 \\ \Leftrightarrow 7x^2 = -1372 \\ \Leftrightarrow x^2 = \frac{-1372}{7} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-10x^2+347=-8x^2+9 \\ \Leftrightarrow -10x^2+8x^2=9-347 \\ \Leftrightarrow -2x^2 = -338 \\ \Leftrightarrow x^2 = \frac{-338}{-2}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
5. \(8x^2-1346=2x^2+4 \\ \Leftrightarrow 8x^2-2x^2=4+1346 \\ \Leftrightarrow 6x^2 = 1350 \\ \Leftrightarrow x^2 = \frac{1350}{6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
6. \(2(-5x^2-9)=-(3x^2+18) \\ \Leftrightarrow -10x^2-18=-3x^2-18 \\ \Leftrightarrow -10x^2+3x^2=-18+18 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-6x^2+201=-2x^2+5 \\ \Leftrightarrow -6x^2+2x^2=5-201 \\ \Leftrightarrow -4x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-4}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
8. \(7x^2-7=0 \\ \Leftrightarrow 7x^2 = 7 \\ \Leftrightarrow x^2 = \frac{7}{7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(-3(-3x^2-10)=-(-11x^2-158) \\ \Leftrightarrow 9x^2+30=11x^2+158 \\ \Leftrightarrow 9x^2-11x^2=158-30 \\ \Leftrightarrow -2x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{-2} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-6x^2-69=-10x^2-5 \\ \Leftrightarrow -6x^2+10x^2=-5+69 \\ \Leftrightarrow 4x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(-11x^2+38=-4x^2+10 \\ \Leftrightarrow -11x^2+4x^2=10-38 \\ \Leftrightarrow -7x^2 = -28 \\ \Leftrightarrow x^2 = \frac{-28}{-7}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(5x^2+709=-2x^2+9 \\ \Leftrightarrow 5x^2+2x^2=9-709 \\ \Leftrightarrow 7x^2 = -700 \\ \Leftrightarrow x^2 = \frac{-700}{7} < 0 \\ V = \varnothing \\ -----------------\)