Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(10x^2-10)=-(26x^2+754)\)
2. \(-4x^2-40=-8x^2-4\)
3. \(-12x^2+398=-7x^2-7\)
4. \(-12x^2+1797=-4x^2-3\)
5. \(3(-8x^2+6)=-(20x^2-14)\)
6. \(4(7x^2+3)=-(-34x^2-228)\)
7. \(-2(-2x^2+9)=-(2x^2-996)\)
8. \(-4x^2+977=4x^2+9\)
9. \(3(-8x^2-4)=-(29x^2-8)\)
10. \(-4(4x^2+5)=-(13x^2-487)\)
11. \(2(-4x^2-5)=-(15x^2-1173)\)
12. \(-x^2+49=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(10x^2-10)=-(26x^2+754) \\ \Leftrightarrow -30x^2+30=-26x^2-754 \\ \Leftrightarrow -30x^2+26x^2=-754-30 \\ \Leftrightarrow -4x^2 = -784 \\ \Leftrightarrow x^2 = \frac{-784}{-4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
2. \(-4x^2-40=-8x^2-4 \\ \Leftrightarrow -4x^2+8x^2=-4+40 \\ \Leftrightarrow 4x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
3. \(-12x^2+398=-7x^2-7 \\ \Leftrightarrow -12x^2+7x^2=-7-398 \\ \Leftrightarrow -5x^2 = -405 \\ \Leftrightarrow x^2 = \frac{-405}{-5}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
4. \(-12x^2+1797=-4x^2-3 \\ \Leftrightarrow -12x^2+4x^2=-3-1797 \\ \Leftrightarrow -8x^2 = -1800 \\ \Leftrightarrow x^2 = \frac{-1800}{-8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
5. \(3(-8x^2+6)=-(20x^2-14) \\ \Leftrightarrow -24x^2+18=-20x^2+14 \\ \Leftrightarrow -24x^2+20x^2=14-18 \\ \Leftrightarrow -4x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(4(7x^2+3)=-(-34x^2-228) \\ \Leftrightarrow 28x^2+12=34x^2+228 \\ \Leftrightarrow 28x^2-34x^2=228-12 \\ \Leftrightarrow -6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{-6} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-2(-2x^2+9)=-(2x^2-996) \\ \Leftrightarrow 4x^2-18=-2x^2+996 \\ \Leftrightarrow 4x^2+2x^2=996+18 \\ \Leftrightarrow 6x^2 = 1014 \\ \Leftrightarrow x^2 = \frac{1014}{6}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
8. \(-4x^2+977=4x^2+9 \\ \Leftrightarrow -4x^2-4x^2=9-977 \\ \Leftrightarrow -8x^2 = -968 \\ \Leftrightarrow x^2 = \frac{-968}{-8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(3(-8x^2-4)=-(29x^2-8) \\ \Leftrightarrow -24x^2-12=-29x^2+8 \\ \Leftrightarrow -24x^2+29x^2=8+12 \\ \Leftrightarrow 5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
10. \(-4(4x^2+5)=-(13x^2-487) \\ \Leftrightarrow -16x^2-20=-13x^2+487 \\ \Leftrightarrow -16x^2+13x^2=487+20 \\ \Leftrightarrow -3x^2 = 507 \\ \Leftrightarrow x^2 = \frac{507}{-3} < 0 \\ V = \varnothing \\ -----------------\)
11. \(2(-4x^2-5)=-(15x^2-1173) \\ \Leftrightarrow -8x^2-10=-15x^2+1173 \\ \Leftrightarrow -8x^2+15x^2=1173+10 \\ \Leftrightarrow 7x^2 = 1183 \\ \Leftrightarrow x^2 = \frac{1183}{7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
12. \(-x^2+49=0 \\ \Leftrightarrow -x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{-1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)