Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-x^2-795=-9x^2+5\)
2. \(5(-7x^2-5)=-(38x^2-23)\)
3. \(5(8x^2-10)=-(-42x^2+50)\)
4. \(-4x^2+0=0\)
5. \(-8x^2+0=0\)
6. \(-x^2-13=-4x^2-10\)
7. \(-12x^2+102=-10x^2+4\)
8. \(4x^2-144=0\)
9. \(-2(-3x^2-7)=-(-12x^2+82)\)
10. \(8x^2+0=0\)
11. \(3x^2-12=0\)
12. \(-3(2x^2-9)=-(2x^2+169)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-x^2-795=-9x^2+5 \\ \Leftrightarrow -x^2+9x^2=5+795 \\ \Leftrightarrow 8x^2 = 800 \\ \Leftrightarrow x^2 = \frac{800}{8}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
2. \(5(-7x^2-5)=-(38x^2-23) \\ \Leftrightarrow -35x^2-25=-38x^2+23 \\ \Leftrightarrow -35x^2+38x^2=23+25 \\ \Leftrightarrow 3x^2 = 48 \\ \Leftrightarrow x^2 = \frac{48}{3}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
3. \(5(8x^2-10)=-(-42x^2+50) \\ \Leftrightarrow 40x^2-50=42x^2-50 \\ \Leftrightarrow 40x^2-42x^2=-50+50 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-4x^2+0=0 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(-8x^2+0=0 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(-x^2-13=-4x^2-10 \\ \Leftrightarrow -x^2+4x^2=-10+13 \\ \Leftrightarrow 3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
7. \(-12x^2+102=-10x^2+4 \\ \Leftrightarrow -12x^2+10x^2=4-102 \\ \Leftrightarrow -2x^2 = -98 \\ \Leftrightarrow x^2 = \frac{-98}{-2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
8. \(4x^2-144=0 \\ \Leftrightarrow 4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
9. \(-2(-3x^2-7)=-(-12x^2+82) \\ \Leftrightarrow 6x^2+14=12x^2-82 \\ \Leftrightarrow 6x^2-12x^2=-82-14 \\ \Leftrightarrow -6x^2 = -96 \\ \Leftrightarrow x^2 = \frac{-96}{-6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
10. \(8x^2+0=0 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(3x^2-12=0 \\ \Leftrightarrow 3x^2 = 12 \\ \Leftrightarrow x^2 = \frac{12}{3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(-3(2x^2-9)=-(2x^2+169) \\ \Leftrightarrow -6x^2+27=-2x^2-169 \\ \Leftrightarrow -6x^2+2x^2=-169-27 \\ \Leftrightarrow -4x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-4}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)