Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(10x^2+4)=-(16x^2+408)\)
2. \(3x^2+683=6x^2+8\)
3. \(3(-6x^2+8)=-(26x^2-536)\)
4. \(-5x^2+0=0\)
5. \(2x^2-200=0\)
6. \(-5x^2-359=-2x^2+4\)
7. \(4(-3x^2-10)=-(19x^2+740)\)
8. \(17x^2-1149=9x^2+3\)
9. \(13x^2+1150=5x^2-2\)
10. \(-6x^2+0=0\)
11. \(x^2+4=0\)
12. \(-2(2x^2-6)=-(7x^2+288)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(10x^2+4)=-(16x^2+408) \\ \Leftrightarrow -20x^2-8=-16x^2-408 \\ \Leftrightarrow -20x^2+16x^2=-408+8 \\ \Leftrightarrow -4x^2 = -400 \\ \Leftrightarrow x^2 = \frac{-400}{-4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
2. \(3x^2+683=6x^2+8 \\ \Leftrightarrow 3x^2-6x^2=8-683 \\ \Leftrightarrow -3x^2 = -675 \\ \Leftrightarrow x^2 = \frac{-675}{-3}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
3. \(3(-6x^2+8)=-(26x^2-536) \\ \Leftrightarrow -18x^2+24=-26x^2+536 \\ \Leftrightarrow -18x^2+26x^2=536-24 \\ \Leftrightarrow 8x^2 = 512 \\ \Leftrightarrow x^2 = \frac{512}{8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
4. \(-5x^2+0=0 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(2x^2-200=0 \\ \Leftrightarrow 2x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{2}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
6. \(-5x^2-359=-2x^2+4 \\ \Leftrightarrow -5x^2+2x^2=4+359 \\ \Leftrightarrow -3x^2 = 363 \\ \Leftrightarrow x^2 = \frac{363}{-3} < 0 \\ V = \varnothing \\ -----------------\)
7. \(4(-3x^2-10)=-(19x^2+740) \\ \Leftrightarrow -12x^2-40=-19x^2-740 \\ \Leftrightarrow -12x^2+19x^2=-740+40 \\ \Leftrightarrow 7x^2 = -700 \\ \Leftrightarrow x^2 = \frac{-700}{7} < 0 \\ V = \varnothing \\ -----------------\)
8. \(17x^2-1149=9x^2+3 \\ \Leftrightarrow 17x^2-9x^2=3+1149 \\ \Leftrightarrow 8x^2 = 1152 \\ \Leftrightarrow x^2 = \frac{1152}{8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
9. \(13x^2+1150=5x^2-2 \\ \Leftrightarrow 13x^2-5x^2=-2-1150 \\ \Leftrightarrow 8x^2 = -1152 \\ \Leftrightarrow x^2 = \frac{-1152}{8} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-6x^2+0=0 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(x^2+4=0 \\ \Leftrightarrow x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{1} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-2(2x^2-6)=-(7x^2+288) \\ \Leftrightarrow -4x^2+12=-7x^2-288 \\ \Leftrightarrow -4x^2+7x^2=-288-12 \\ \Leftrightarrow 3x^2 = -300 \\ \Leftrightarrow x^2 = \frac{-300}{3} < 0 \\ V = \varnothing \\ -----------------\)