Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2-32=0\)
2. \(-5x^2+5=0\)
3. \(9x^2-20=10x^2-4\)
4. \(-3x^2-43=-7x^2-7\)
5. \(3(6x^2+10)=-(-17x^2-111)\)
6. \(-x^2+9=0\)
7. \(2x^2-64=-6x^2+8\)
8. \(-2x^2+128=0\)
9. \(3x^2+0=0\)
10. \(12x^2-504=4x^2+8\)
11. \(5(-8x^2+8)=-(34x^2-526)\)
12. \(5(7x^2-6)=-(-34x^2+30)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2-32=0 \\ \Leftrightarrow -8x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{-8} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-5x^2+5=0 \\ \Leftrightarrow -5x^2 = -5 \\ \Leftrightarrow x^2 = \frac{-5}{-5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
3. \(9x^2-20=10x^2-4 \\ \Leftrightarrow 9x^2-10x^2=-4+20 \\ \Leftrightarrow -x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{-1} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-3x^2-43=-7x^2-7 \\ \Leftrightarrow -3x^2+7x^2=-7+43 \\ \Leftrightarrow 4x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
5. \(3(6x^2+10)=-(-17x^2-111) \\ \Leftrightarrow 18x^2+30=17x^2+111 \\ \Leftrightarrow 18x^2-17x^2=111-30 \\ \Leftrightarrow x^2 = 81 \\ \Leftrightarrow x^2 = \frac{81}{1}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
6. \(-x^2+9=0 \\ \Leftrightarrow -x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{-1}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
7. \(2x^2-64=-6x^2+8 \\ \Leftrightarrow 2x^2+6x^2=8+64 \\ \Leftrightarrow 8x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{8}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
8. \(-2x^2+128=0 \\ \Leftrightarrow -2x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
9. \(3x^2+0=0 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(12x^2-504=4x^2+8 \\ \Leftrightarrow 12x^2-4x^2=8+504 \\ \Leftrightarrow 8x^2 = 512 \\ \Leftrightarrow x^2 = \frac{512}{8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
11. \(5(-8x^2+8)=-(34x^2-526) \\ \Leftrightarrow -40x^2+40=-34x^2+526 \\ \Leftrightarrow -40x^2+34x^2=526-40 \\ \Leftrightarrow -6x^2 = 486 \\ \Leftrightarrow x^2 = \frac{486}{-6} < 0 \\ V = \varnothing \\ -----------------\)
12. \(5(7x^2-6)=-(-34x^2+30) \\ \Leftrightarrow 35x^2-30=34x^2-30 \\ \Leftrightarrow 35x^2-34x^2=-30+30 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)