Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2+784=0\)
2. \(2(3x^2-2)=-(-4x^2-446)\)
3. \(-4(-3x^2+6)=-(-20x^2+312)\)
4. \(3x^2+6=2x^2+5\)
5. \(-4(7x^2+8)=-(22x^2-694)\)
6. \(-2(10x^2+6)=-(24x^2+268)\)
7. \(-8x^2+1568=0\)
8. \(-2x^2+68=6x^2-4\)
9. \(-9x^2-593=-6x^2-5\)
10. \(5x^2-1125=0\)
11. \(-x^2-25=0\)
12. \(-5x^2+53=-10x^2+8\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2+784=0 \\ \Leftrightarrow -4x^2 = -784 \\ \Leftrightarrow x^2 = \frac{-784}{-4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
2. \(2(3x^2-2)=-(-4x^2-446) \\ \Leftrightarrow 6x^2-4=4x^2+446 \\ \Leftrightarrow 6x^2-4x^2=446+4 \\ \Leftrightarrow 2x^2 = 450 \\ \Leftrightarrow x^2 = \frac{450}{2}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
3. \(-4(-3x^2+6)=-(-20x^2+312) \\ \Leftrightarrow 12x^2-24=20x^2-312 \\ \Leftrightarrow 12x^2-20x^2=-312+24 \\ \Leftrightarrow -8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
4. \(3x^2+6=2x^2+5 \\ \Leftrightarrow 3x^2-2x^2=5-6 \\ \Leftrightarrow x^2 = -1 \\ \Leftrightarrow x^2 = \frac{-1}{1} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-4(7x^2+8)=-(22x^2-694) \\ \Leftrightarrow -28x^2-32=-22x^2+694 \\ \Leftrightarrow -28x^2+22x^2=694+32 \\ \Leftrightarrow -6x^2 = 726 \\ \Leftrightarrow x^2 = \frac{726}{-6} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-2(10x^2+6)=-(24x^2+268) \\ \Leftrightarrow -20x^2-12=-24x^2-268 \\ \Leftrightarrow -20x^2+24x^2=-268+12 \\ \Leftrightarrow 4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{4} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-8x^2+1568=0 \\ \Leftrightarrow -8x^2 = -1568 \\ \Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
8. \(-2x^2+68=6x^2-4 \\ \Leftrightarrow -2x^2-6x^2=-4-68 \\ \Leftrightarrow -8x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-8}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
9. \(-9x^2-593=-6x^2-5 \\ \Leftrightarrow -9x^2+6x^2=-5+593 \\ \Leftrightarrow -3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{-3} < 0 \\ V = \varnothing \\ -----------------\)
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. \(-x^2-25=0 \\ \Leftrightarrow -x^2 = 25 \\ \Leftrightarrow x^2 = \frac{25}{-1} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-5x^2+53=-10x^2+8 \\ \Leftrightarrow -5x^2+10x^2=8-53 \\ \Leftrightarrow 5x^2 = -45 \\ \Leftrightarrow x^2 = \frac{-45}{5} < 0 \\ V = \varnothing \\ -----------------\)