Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5x^2-153=-8x^2-6\)
2. \(3(4x^2-8)=-(-20x^2+56)\)
3. \(x^2-840=-6x^2+7\)
4. \(x^2-144=0\)
5. \(-x^2-28=-9x^2+4\)
6. \(3(5x^2-8)=-(-12x^2-483)\)
7. \(6x^2-477=10x^2+7\)
8. \(5x^2+105=7x^2+7\)
9. \(5x^2-980=0\)
10. \(2x^2-392=0\)
11. \(3x^2-75=0\)
12. \(4(2x^2+8)=-(-13x^2+948)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5x^2-153=-8x^2-6 \\ \Leftrightarrow -5x^2+8x^2=-6+153 \\ \Leftrightarrow 3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{3}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(3(4x^2-8)=-(-20x^2+56) \\ \Leftrightarrow 12x^2-24=20x^2-56 \\ \Leftrightarrow 12x^2-20x^2=-56+24 \\ \Leftrightarrow -8x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{-8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
3. \(x^2-840=-6x^2+7 \\ \Leftrightarrow x^2+6x^2=7+840 \\ \Leftrightarrow 7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
4. \(x^2-144=0 \\ \Leftrightarrow x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{1}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
5. \(-x^2-28=-9x^2+4 \\ \Leftrightarrow -x^2+9x^2=4+28 \\ \Leftrightarrow 8x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
6. \(3(5x^2-8)=-(-12x^2-483) \\ \Leftrightarrow 15x^2-24=12x^2+483 \\ \Leftrightarrow 15x^2-12x^2=483+24 \\ \Leftrightarrow 3x^2 = 507 \\ \Leftrightarrow x^2 = \frac{507}{3}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
7. \(6x^2-477=10x^2+7 \\ \Leftrightarrow 6x^2-10x^2=7+477 \\ \Leftrightarrow -4x^2 = 484 \\ \Leftrightarrow x^2 = \frac{484}{-4} < 0 \\ V = \varnothing \\ -----------------\)
8. \(5x^2+105=7x^2+7 \\ \Leftrightarrow 5x^2-7x^2=7-105 \\ \Leftrightarrow -2x^2 = -98 \\ \Leftrightarrow x^2 = \frac{-98}{-2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
9. \(5x^2-980=0 \\ \Leftrightarrow 5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
10. \(2x^2-392=0 \\ \Leftrightarrow 2x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{2}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
11. \(3x^2-75=0 \\ \Leftrightarrow 3x^2 = 75 \\ \Leftrightarrow x^2 = \frac{75}{3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
12. \(4(2x^2+8)=-(-13x^2+948) \\ \Leftrightarrow 8x^2+32=13x^2-948 \\ \Leftrightarrow 8x^2-13x^2=-948-32 \\ \Leftrightarrow -5x^2 = -980 \\ \Leftrightarrow x^2 = \frac{-980}{-5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)