Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(14x^2-385=6x^2+7\)
2. \(3x^2-27=0\)
3. \(4x^2+64=0\)
4. \(-3(-5x^2+10)=-(-13x^2-420)\)
5. \(-5(5x^2+2)=-(24x^2+9)\)
6. \(-3x^2-9=-4x^2-9\)
7. \(4x^2-713=9x^2+7\)
8. \(-2(7x^2-3)=-(20x^2-6)\)
9. \(-4(8x^2-2)=-(39x^2-1583)\)
10. \(-3x^2-1023=3x^2-9\)
11. \(-8x^2-1152=0\)
12. \(-5(-8x^2-10)=-(-47x^2-750)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(14x^2-385=6x^2+7 \\ \Leftrightarrow 14x^2-6x^2=7+385 \\ \Leftrightarrow 8x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{8}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(3x^2-27=0 \\ \Leftrightarrow 3x^2 = 27 \\ \Leftrightarrow x^2 = \frac{27}{3}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
3. \(4x^2+64=0 \\ \Leftrightarrow 4x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{4} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-3(-5x^2+10)=-(-13x^2-420) \\ \Leftrightarrow 15x^2-30=13x^2+420 \\ \Leftrightarrow 15x^2-13x^2=420+30 \\ \Leftrightarrow 2x^2 = 450 \\ \Leftrightarrow x^2 = \frac{450}{2}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
5. \(-5(5x^2+2)=-(24x^2+9) \\ \Leftrightarrow -25x^2-10=-24x^2-9 \\ \Leftrightarrow -25x^2+24x^2=-9+10 \\ \Leftrightarrow -x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{-1} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-3x^2-9=-4x^2-9 \\ \Leftrightarrow -3x^2+4x^2=-9+9 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(4x^2-713=9x^2+7 \\ \Leftrightarrow 4x^2-9x^2=7+713 \\ \Leftrightarrow -5x^2 = 720 \\ \Leftrightarrow x^2 = \frac{720}{-5} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-2(7x^2-3)=-(20x^2-6) \\ \Leftrightarrow -14x^2+6=-20x^2+6 \\ \Leftrightarrow -14x^2+20x^2=6-6 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(-4(8x^2-2)=-(39x^2-1583) \\ \Leftrightarrow -32x^2+8=-39x^2+1583 \\ \Leftrightarrow -32x^2+39x^2=1583-8 \\ \Leftrightarrow 7x^2 = 1575 \\ \Leftrightarrow x^2 = \frac{1575}{7}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
10. \(-3x^2-1023=3x^2-9 \\ \Leftrightarrow -3x^2-3x^2=-9+1023 \\ \Leftrightarrow -6x^2 = 1014 \\ \Leftrightarrow x^2 = \frac{1014}{-6} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-8x^2-1152=0 \\ \Leftrightarrow -8x^2 = 1152 \\ \Leftrightarrow x^2 = \frac{1152}{-8} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-5(-8x^2-10)=-(-47x^2-750) \\ \Leftrightarrow 40x^2+50=47x^2+750 \\ \Leftrightarrow 40x^2-47x^2=750-50 \\ \Leftrightarrow -7x^2 = 700 \\ \Leftrightarrow x^2 = \frac{700}{-7} < 0 \\ V = \varnothing \\ -----------------\)