Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(-5x^2+4)=-(6x^2-44)\)
2. \(3(-3x^2-2)=-(11x^2+6)\)
3. \(5(9x^2-3)=-(-42x^2-660)\)
4. \(-7x^2+67=-5x^2-5\)
5. \(-13x^2-140=-9x^2+4\)
6. \(-x^2-100=0\)
7. \(4(-8x^2+9)=-(28x^2+0)\)
8. \(2(-4x^2+3)=-(2x^2+858)\)
9. \(x^2+49=0\)
10. \(2x^2+450=0\)
11. \(2(-10x^2-6)=-(19x^2-109)\)
12. \(3x^2-718=9x^2+8\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(-5x^2+4)=-(6x^2-44) \\ \Leftrightarrow -10x^2+8=-6x^2+44 \\ \Leftrightarrow -10x^2+6x^2=44-8 \\ \Leftrightarrow -4x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{-4} < 0 \\ V = \varnothing \\ -----------------\)
2. \(3(-3x^2-2)=-(11x^2+6) \\ \Leftrightarrow -9x^2-6=-11x^2-6 \\ \Leftrightarrow -9x^2+11x^2=-6+6 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(5(9x^2-3)=-(-42x^2-660) \\ \Leftrightarrow 45x^2-15=42x^2+660 \\ \Leftrightarrow 45x^2-42x^2=660+15 \\ \Leftrightarrow 3x^2 = 675 \\ \Leftrightarrow x^2 = \frac{675}{3}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
4. \(-7x^2+67=-5x^2-5 \\ \Leftrightarrow -7x^2+5x^2=-5-67 \\ \Leftrightarrow -2x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-2}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
5. \(-13x^2-140=-9x^2+4 \\ \Leftrightarrow -13x^2+9x^2=4+140 \\ \Leftrightarrow -4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{-4} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-x^2-100=0 \\ \Leftrightarrow -x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{-1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(4(-8x^2+9)=-(28x^2+0) \\ \Leftrightarrow -32x^2+36=-28x^2+0 \\ \Leftrightarrow -32x^2+28x^2=0-36 \\ \Leftrightarrow -4x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
8. \(2(-4x^2+3)=-(2x^2+858) \\ \Leftrightarrow -8x^2+6=-2x^2-858 \\ \Leftrightarrow -8x^2+2x^2=-858-6 \\ \Leftrightarrow -6x^2 = -864 \\ \Leftrightarrow x^2 = \frac{-864}{-6}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
9. \(x^2+49=0 \\ \Leftrightarrow x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{1} < 0 \\ V = \varnothing \\ -----------------\)
10. \(2x^2+450=0 \\ \Leftrightarrow 2x^2 = -450 \\ \Leftrightarrow x^2 = \frac{-450}{2} < 0 \\ V = \varnothing \\ -----------------\)
11. \(2(-10x^2-6)=-(19x^2-109) \\ \Leftrightarrow -20x^2-12=-19x^2+109 \\ \Leftrightarrow -20x^2+19x^2=109+12 \\ \Leftrightarrow -x^2 = 121 \\ \Leftrightarrow x^2 = \frac{121}{-1} < 0 \\ V = \varnothing \\ -----------------\)
12. \(3x^2-718=9x^2+8 \\ \Leftrightarrow 3x^2-9x^2=8+718 \\ \Leftrightarrow -6x^2 = 726 \\ \Leftrightarrow x^2 = \frac{726}{-6} < 0 \\ V = \varnothing \\ -----------------\)