Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(8x^2+4)=-(-35x^2-124)\)
2. \(3x^2+137=-5x^2+9\)
3. \(-14x^2+790=-10x^2+6\)
4. \(3(4x^2-3)=-(-11x^2+130)\)
5. \(3(10x^2+7)=-(-38x^2-13)\)
6. \(-5(7x^2-6)=-(33x^2-48)\)
7. \(-3x^2-588=0\)
8. \(-11x^2-411=-6x^2-6\)
9. \(3(8x^2-3)=-(-20x^2-891)\)
10. \(2(3x^2+2)=-(-2x^2+140)\)
11. \(-4(-3x^2+2)=-(-8x^2+8)\)
12. \(5(4x^2-10)=-(-12x^2+50)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(8x^2+4)=-(-35x^2-124) \\ \Leftrightarrow 32x^2+16=35x^2+124 \\ \Leftrightarrow 32x^2-35x^2=124-16 \\ \Leftrightarrow -3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{-3} < 0 \\ V = \varnothing \\ -----------------\)
2. \(3x^2+137=-5x^2+9 \\ \Leftrightarrow 3x^2+5x^2=9-137 \\ \Leftrightarrow 8x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{8} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-14x^2+790=-10x^2+6 \\ \Leftrightarrow -14x^2+10x^2=6-790 \\ \Leftrightarrow -4x^2 = -784 \\ \Leftrightarrow x^2 = \frac{-784}{-4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
4. \(3(4x^2-3)=-(-11x^2+130) \\ \Leftrightarrow 12x^2-9=11x^2-130 \\ \Leftrightarrow 12x^2-11x^2=-130+9 \\ \Leftrightarrow x^2 = -121 \\ \Leftrightarrow x^2 = \frac{-121}{1} < 0 \\ V = \varnothing \\ -----------------\)
5. \(3(10x^2+7)=-(-38x^2-13) \\ \Leftrightarrow 30x^2+21=38x^2+13 \\ \Leftrightarrow 30x^2-38x^2=13-21 \\ \Leftrightarrow -8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(-5(7x^2-6)=-(33x^2-48) \\ \Leftrightarrow -35x^2+30=-33x^2+48 \\ \Leftrightarrow -35x^2+33x^2=48-30 \\ \Leftrightarrow -2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{-2} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-3x^2-588=0 \\ \Leftrightarrow -3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{-3} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-11x^2-411=-6x^2-6 \\ \Leftrightarrow -11x^2+6x^2=-6+411 \\ \Leftrightarrow -5x^2 = 405 \\ \Leftrightarrow x^2 = \frac{405}{-5} < 0 \\ V = \varnothing \\ -----------------\)
9. \(3(8x^2-3)=-(-20x^2-891) \\ \Leftrightarrow 24x^2-9=20x^2+891 \\ \Leftrightarrow 24x^2-20x^2=891+9 \\ \Leftrightarrow 4x^2 = 900 \\ \Leftrightarrow x^2 = \frac{900}{4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
10. \(2(3x^2+2)=-(-2x^2+140) \\ \Leftrightarrow 6x^2+4=2x^2-140 \\ \Leftrightarrow 6x^2-2x^2=-140-4 \\ \Leftrightarrow 4x^2 = -144 \\ \Leftrightarrow x^2 = \frac{-144}{4} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-4(-3x^2+2)=-(-8x^2+8) \\ \Leftrightarrow 12x^2-8=8x^2-8 \\ \Leftrightarrow 12x^2-8x^2=-8+8 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(5(4x^2-10)=-(-12x^2+50) \\ \Leftrightarrow 20x^2-50=12x^2-50 \\ \Leftrightarrow 20x^2-12x^2=-50+50 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)