Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2-174=-9x^2+6\)
2. \(-11x^2+283=-3x^2-5\)
3. \(-x^2+0=0\)
4. \(2x^2-570=-5x^2-3\)
5. \(4x^2-9=6x^2+9\)
6. \(4(-5x^2+4)=-(14x^2-232)\)
7. \(5x^2+245=0\)
8. \(-x^2-169=0\)
9. \(-x^2+4=0\)
10. \(7x^2-11=4x^2-8\)
11. \(7x^2+700=0\)
12. \(5(4x^2+4)=-(-13x^2-272)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2-174=-9x^2+6 \\ \Leftrightarrow -4x^2+9x^2=6+174 \\ \Leftrightarrow 5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
2. \(-11x^2+283=-3x^2-5 \\ \Leftrightarrow -11x^2+3x^2=-5-283 \\ \Leftrightarrow -8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
3. \(-x^2+0=0 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(2x^2-570=-5x^2-3 \\ \Leftrightarrow 2x^2+5x^2=-3+570 \\ \Leftrightarrow 7x^2 = 567 \\ \Leftrightarrow x^2 = \frac{567}{7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
5. \(4x^2-9=6x^2+9 \\ \Leftrightarrow 4x^2-6x^2=9+9 \\ \Leftrightarrow -2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{-2} < 0 \\ V = \varnothing \\ -----------------\)
6. \(4(-5x^2+4)=-(14x^2-232) \\ \Leftrightarrow -20x^2+16=-14x^2+232 \\ \Leftrightarrow -20x^2+14x^2=232-16 \\ \Leftrightarrow -6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{-6} < 0 \\ V = \varnothing \\ -----------------\)
7. \(5x^2+245=0 \\ \Leftrightarrow 5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{5} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-x^2-169=0 \\ \Leftrightarrow -x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{-1} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-x^2+4=0 \\ \Leftrightarrow -x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-1}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
10. \(7x^2-11=4x^2-8 \\ \Leftrightarrow 7x^2-4x^2=-8+11 \\ \Leftrightarrow 3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
11. \(7x^2+700=0 \\ \Leftrightarrow 7x^2 = -700 \\ \Leftrightarrow x^2 = \frac{-700}{7} < 0 \\ V = \varnothing \\ -----------------\)
12. \(5(4x^2+4)=-(-13x^2-272) \\ \Leftrightarrow 20x^2+20=13x^2+272 \\ \Leftrightarrow 20x^2-13x^2=272-20 \\ \Leftrightarrow 7x^2 = 252 \\ \Leftrightarrow x^2 = \frac{252}{7}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)