Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-7x^2+1372=0\)
2. \(x^2+64=0\)
3. \(-3x^2-241=2x^2+4\)
4. \(-7x^2+28=0\)
5. \(4x^2-60=-3x^2+3\)
6. \(-4(8x^2+8)=-(35x^2+29)\)
7. \(8x^2-122=3x^2+3\)
8. \(-4(-8x^2-4)=-(-38x^2-70)\)
9. \(-11x^2+12=-6x^2-8\)
10. \(2(-9x^2-4)=-(15x^2+440)\)
11. \(-3x^2+50=3x^2-4\)
12. \(-3x^2+260=4x^2+8\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-7x^2+1372=0 \\ \Leftrightarrow -7x^2 = -1372 \\ \Leftrightarrow x^2 = \frac{-1372}{-7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
2. \(x^2+64=0 \\ \Leftrightarrow x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{1} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-3x^2-241=2x^2+4 \\ \Leftrightarrow -3x^2-2x^2=4+241 \\ \Leftrightarrow -5x^2 = 245 \\ \Leftrightarrow x^2 = \frac{245}{-5} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-7x^2+28=0 \\ \Leftrightarrow -7x^2 = -28 \\ \Leftrightarrow x^2 = \frac{-28}{-7}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
5. \(4x^2-60=-3x^2+3 \\ \Leftrightarrow 4x^2+3x^2=3+60 \\ \Leftrightarrow 7x^2 = 63 \\ \Leftrightarrow x^2 = \frac{63}{7}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
6. \(-4(8x^2+8)=-(35x^2+29) \\ \Leftrightarrow -32x^2-32=-35x^2-29 \\ \Leftrightarrow -32x^2+35x^2=-29+32 \\ \Leftrightarrow 3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
7. \(8x^2-122=3x^2+3 \\ \Leftrightarrow 8x^2-3x^2=3+122 \\ \Leftrightarrow 5x^2 = 125 \\ \Leftrightarrow x^2 = \frac{125}{5}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
8. \(-4(-8x^2-4)=-(-38x^2-70) \\ \Leftrightarrow 32x^2+16=38x^2+70 \\ \Leftrightarrow 32x^2-38x^2=70-16 \\ \Leftrightarrow -6x^2 = 54 \\ \Leftrightarrow x^2 = \frac{54}{-6} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-11x^2+12=-6x^2-8 \\ \Leftrightarrow -11x^2+6x^2=-8-12 \\ \Leftrightarrow -5x^2 = -20 \\ \Leftrightarrow x^2 = \frac{-20}{-5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
10. \(2(-9x^2-4)=-(15x^2+440) \\ \Leftrightarrow -18x^2-8=-15x^2-440 \\ \Leftrightarrow -18x^2+15x^2=-440+8 \\ \Leftrightarrow -3x^2 = -432 \\ \Leftrightarrow x^2 = \frac{-432}{-3}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
11. \(-3x^2+50=3x^2-4 \\ \Leftrightarrow -3x^2-3x^2=-4-50 \\ \Leftrightarrow -6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{-6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
12. \(-3x^2+260=4x^2+8 \\ \Leftrightarrow -3x^2-4x^2=8-260 \\ \Leftrightarrow -7x^2 = -252 \\ \Leftrightarrow x^2 = \frac{-252}{-7}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)