Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2+200=0\)
2. \(-4x^2+16=0\)
3. \(-8x^2+0=0\)
4. \(-x^2-81=0\)
5. \(-3(-6x^2+8)=-(-11x^2+136)\)
6. \(3x^2+432=0\)
7. \(-4x^2+64=0\)
8. \(-14x^2+238=-9x^2-7\)
9. \(-2(-7x^2-9)=-(-22x^2-90)\)
10. \(-5(7x^2-10)=-(40x^2-655)\)
11. \(-3x^2+161=-4x^2-8\)
12. \(4(-8x^2+2)=-(25x^2+335)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2+200=0 \\ \Leftrightarrow -8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
2. \(-4x^2+16=0 \\ \Leftrightarrow -4x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{-4}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
3. \(-8x^2+0=0 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-x^2-81=0 \\ \Leftrightarrow -x^2 = 81 \\ \Leftrightarrow x^2 = \frac{81}{-1} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-3(-6x^2+8)=-(-11x^2+136) \\ \Leftrightarrow 18x^2-24=11x^2-136 \\ \Leftrightarrow 18x^2-11x^2=-136+24 \\ \Leftrightarrow 7x^2 = -112 \\ \Leftrightarrow x^2 = \frac{-112}{7} < 0 \\ V = \varnothing \\ -----------------\)
6. \(3x^2+432=0 \\ \Leftrightarrow 3x^2 = -432 \\ \Leftrightarrow x^2 = \frac{-432}{3} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-4x^2+64=0 \\ \Leftrightarrow -4x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
8. \(-14x^2+238=-9x^2-7 \\ \Leftrightarrow -14x^2+9x^2=-7-238 \\ \Leftrightarrow -5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{-5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
9. \(-2(-7x^2-9)=-(-22x^2-90) \\ \Leftrightarrow 14x^2+18=22x^2+90 \\ \Leftrightarrow 14x^2-22x^2=90-18 \\ \Leftrightarrow -8x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{-8} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-5(7x^2-10)=-(40x^2-655) \\ \Leftrightarrow -35x^2+50=-40x^2+655 \\ \Leftrightarrow -35x^2+40x^2=655-50 \\ \Leftrightarrow 5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
11. \(-3x^2+161=-4x^2-8 \\ \Leftrightarrow -3x^2+4x^2=-8-161 \\ \Leftrightarrow x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{1} < 0 \\ V = \varnothing \\ -----------------\)
12. \(4(-8x^2+2)=-(25x^2+335) \\ \Leftrightarrow -32x^2+8=-25x^2-335 \\ \Leftrightarrow -32x^2+25x^2=-335-8 \\ \Leftrightarrow -7x^2 = -343 \\ \Leftrightarrow x^2 = \frac{-343}{-7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)