Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5x^2+80=0\)
2. \(5x^2+388=3x^2-4\)
3. \(2(-5x^2-2)=-(2x^2-508)\)
4. \(-x^2-64=0\)
5. \(-3(4x^2-3)=-(14x^2-107)\)
6. \(7x^2+63=0\)
7. \(x^2+56=2x^2+7\)
8. \(x^2+9=0\)
9. \(4(7x^2+3)=-(-31x^2+15)\)
10. \(5x^2-1125=0\)
11. \(-3x^2+243=0\)
12. \(6x^2-32=2x^2+4\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5x^2+80=0 \\ \Leftrightarrow -5x^2 = -80 \\ \Leftrightarrow x^2 = \frac{-80}{-5}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
2. \(5x^2+388=3x^2-4 \\ \Leftrightarrow 5x^2-3x^2=-4-388 \\ \Leftrightarrow 2x^2 = -392 \\ \Leftrightarrow x^2 = \frac{-392}{2} < 0 \\ V = \varnothing \\ -----------------\)
3. \(2(-5x^2-2)=-(2x^2-508) \\ \Leftrightarrow -10x^2-4=-2x^2+508 \\ \Leftrightarrow -10x^2+2x^2=508+4 \\ \Leftrightarrow -8x^2 = 512 \\ \Leftrightarrow x^2 = \frac{512}{-8} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-x^2-64=0 \\ \Leftrightarrow -x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{-1} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-3(4x^2-3)=-(14x^2-107) \\ \Leftrightarrow -12x^2+9=-14x^2+107 \\ \Leftrightarrow -12x^2+14x^2=107-9 \\ \Leftrightarrow 2x^2 = 98 \\ \Leftrightarrow x^2 = \frac{98}{2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
6. \(7x^2+63=0 \\ \Leftrightarrow 7x^2 = -63 \\ \Leftrightarrow x^2 = \frac{-63}{7} < 0 \\ V = \varnothing \\ -----------------\)
7. \(x^2+56=2x^2+7 \\ \Leftrightarrow x^2-2x^2=7-56 \\ \Leftrightarrow -x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{-1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
8. \(x^2+9=0 \\ \Leftrightarrow x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{1} < 0 \\ V = \varnothing \\ -----------------\)
9. \(4(7x^2+3)=-(-31x^2+15) \\ \Leftrightarrow 28x^2+12=31x^2-15 \\ \Leftrightarrow 28x^2-31x^2=-15-12 \\ \Leftrightarrow -3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{-3}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
10. \(5x^2-1125=0 \\ \Leftrightarrow 5x^2 = 1125 \\ \Leftrightarrow x^2 = \frac{1125}{5}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
11. \(-3x^2+243=0 \\ \Leftrightarrow -3x^2 = -243 \\ \Leftrightarrow x^2 = \frac{-243}{-3}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
12. \(6x^2-32=2x^2+4 \\ \Leftrightarrow 6x^2-2x^2=4+32 \\ \Leftrightarrow 4x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)