Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(10x^2+7)=-(-51x^2-36)\)
2. \(13x^2-77=10x^2-2\)
3. \(4(7x^2-5)=-(-24x^2-764)\)
4. \(-2(10x^2-8)=-(16x^2-916)\)
5. \(-6x^2+216=0\)
6. \(-x^2-652=-9x^2-4\)
7. \(6x^2-600=0\)
8. \(3x^2+47=8x^2+2\)
9. \(5(6x^2+7)=-(-32x^2-35)\)
10. \(-2x^2+162=0\)
11. \(13x^2+503=5x^2-9\)
12. \(-2x^2+481=4x^2-5\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(10x^2+7)=-(-51x^2-36) \\ \Leftrightarrow 50x^2+35=51x^2+36 \\ \Leftrightarrow 50x^2-51x^2=36-35 \\ \Leftrightarrow -x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{-1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(13x^2-77=10x^2-2 \\ \Leftrightarrow 13x^2-10x^2=-2+77 \\ \Leftrightarrow 3x^2 = 75 \\ \Leftrightarrow x^2 = \frac{75}{3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
3. \(4(7x^2-5)=-(-24x^2-764) \\ \Leftrightarrow 28x^2-20=24x^2+764 \\ \Leftrightarrow 28x^2-24x^2=764+20 \\ \Leftrightarrow 4x^2 = 784 \\ \Leftrightarrow x^2 = \frac{784}{4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
4. \(-2(10x^2-8)=-(16x^2-916) \\ \Leftrightarrow -20x^2+16=-16x^2+916 \\ \Leftrightarrow -20x^2+16x^2=916-16 \\ \Leftrightarrow -4x^2 = 900 \\ \Leftrightarrow x^2 = \frac{900}{-4} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-6x^2+216=0 \\ \Leftrightarrow -6x^2 = -216 \\ \Leftrightarrow x^2 = \frac{-216}{-6}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
6. \(-x^2-652=-9x^2-4 \\ \Leftrightarrow -x^2+9x^2=-4+652 \\ \Leftrightarrow 8x^2 = 648 \\ \Leftrightarrow x^2 = \frac{648}{8}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
7. \(6x^2-600=0 \\ \Leftrightarrow 6x^2 = 600 \\ \Leftrightarrow x^2 = \frac{600}{6}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
8. \(3x^2+47=8x^2+2 \\ \Leftrightarrow 3x^2-8x^2=2-47 \\ \Leftrightarrow -5x^2 = -45 \\ \Leftrightarrow x^2 = \frac{-45}{-5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
9. \(5(6x^2+7)=-(-32x^2-35) \\ \Leftrightarrow 30x^2+35=32x^2+35 \\ \Leftrightarrow 30x^2-32x^2=35-35 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(-2x^2+162=0 \\ \Leftrightarrow -2x^2 = -162 \\ \Leftrightarrow x^2 = \frac{-162}{-2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
11. \(13x^2+503=5x^2-9 \\ \Leftrightarrow 13x^2-5x^2=-9-503 \\ \Leftrightarrow 8x^2 = -512 \\ \Leftrightarrow x^2 = \frac{-512}{8} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-2x^2+481=4x^2-5 \\ \Leftrightarrow -2x^2-4x^2=-5-481 \\ \Leftrightarrow -6x^2 = -486 \\ \Leftrightarrow x^2 = \frac{-486}{-6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)