Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(-10x^2+2)=-(-19x^2+3)\)
2. \(3(-4x^2+5)=-(6x^2+9)\)
3. \(-7x^2+343=0\)
4. \(2(-7x^2+3)=-(13x^2+190)\)
5. \(-4x^2+165=-5x^2-4\)
6. \(-2(2x^2-6)=-(0x^2+772)\)
7. \(-3(8x^2+6)=-(28x^2+2)\)
8. \(-3(-9x^2+8)=-(-26x^2+73)\)
9. \(-5(-9x^2+9)=-(-37x^2+45)\)
10. \(14x^2-238=9x^2+7\)
11. \(5(9x^2+7)=-(-44x^2-71)\)
12. \(4(-5x^2+10)=-(14x^2+254)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(-10x^2+2)=-(-19x^2+3) \\ \Leftrightarrow 20x^2-4=19x^2-3 \\ \Leftrightarrow 20x^2-19x^2=-3+4 \\ \Leftrightarrow x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{1}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
2. \(3(-4x^2+5)=-(6x^2+9) \\ \Leftrightarrow -12x^2+15=-6x^2-9 \\ \Leftrightarrow -12x^2+6x^2=-9-15 \\ \Leftrightarrow -6x^2 = -24 \\ \Leftrightarrow x^2 = \frac{-24}{-6}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
3. \(-7x^2+343=0 \\ \Leftrightarrow -7x^2 = -343 \\ \Leftrightarrow x^2 = \frac{-343}{-7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
4. \(2(-7x^2+3)=-(13x^2+190) \\ \Leftrightarrow -14x^2+6=-13x^2-190 \\ \Leftrightarrow -14x^2+13x^2=-190-6 \\ \Leftrightarrow -x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
5. \(-4x^2+165=-5x^2-4 \\ \Leftrightarrow -4x^2+5x^2=-4-165 \\ \Leftrightarrow x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{1} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-2(2x^2-6)=-(0x^2+772) \\ \Leftrightarrow -4x^2+12=0x^2-772 \\ \Leftrightarrow -4x^2+0x^2=-772-12 \\ \Leftrightarrow -4x^2 = -784 \\ \Leftrightarrow x^2 = \frac{-784}{-4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
7. \(-3(8x^2+6)=-(28x^2+2) \\ \Leftrightarrow -24x^2-18=-28x^2-2 \\ \Leftrightarrow -24x^2+28x^2=-2+18 \\ \Leftrightarrow 4x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{4}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
8. \(-3(-9x^2+8)=-(-26x^2+73) \\ \Leftrightarrow 27x^2-24=26x^2-73 \\ \Leftrightarrow 27x^2-26x^2=-73+24 \\ \Leftrightarrow x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{1} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-5(-9x^2+9)=-(-37x^2+45) \\ \Leftrightarrow 45x^2-45=37x^2-45 \\ \Leftrightarrow 45x^2-37x^2=-45+45 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(14x^2-238=9x^2+7 \\ \Leftrightarrow 14x^2-9x^2=7+238 \\ \Leftrightarrow 5x^2 = 245 \\ \Leftrightarrow x^2 = \frac{245}{5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
11. \(5(9x^2+7)=-(-44x^2-71) \\ \Leftrightarrow 45x^2+35=44x^2+71 \\ \Leftrightarrow 45x^2-44x^2=71-35 \\ \Leftrightarrow x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{1}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
12. \(4(-5x^2+10)=-(14x^2+254) \\ \Leftrightarrow -20x^2+40=-14x^2-254 \\ \Leftrightarrow -20x^2+14x^2=-254-40 \\ \Leftrightarrow -6x^2 = -294 \\ \Leftrightarrow x^2 = \frac{-294}{-6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)