Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(6x^2+10)=-(10x^2+118)\)
2. \(3(-6x^2+2)=-(19x^2-6)\)
3. \(4(-7x^2-10)=-(30x^2+40)\)
4. \(5x^2+400=10x^2-5\)
5. \(2x^2-32=0\)
6. \(3(2x^2-8)=-(-3x^2+699)\)
7. \(-3x^2+75=0\)
8. \(3(6x^2+2)=-(-20x^2+2)\)
9. \(-8x^2+8=0\)
10. \(13x^2-1180=6x^2+3\)
11. \(13x^2+291=5x^2+3\)
12. \(4(-9x^2+4)=-(31x^2+304)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(6x^2+10)=-(10x^2+118) \\ \Leftrightarrow -12x^2-20=-10x^2-118 \\ \Leftrightarrow -12x^2+10x^2=-118+20 \\ \Leftrightarrow -2x^2 = -98 \\ \Leftrightarrow x^2 = \frac{-98}{-2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(3(-6x^2+2)=-(19x^2-6) \\ \Leftrightarrow -18x^2+6=-19x^2+6 \\ \Leftrightarrow -18x^2+19x^2=6-6 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(4(-7x^2-10)=-(30x^2+40) \\ \Leftrightarrow -28x^2-40=-30x^2-40 \\ \Leftrightarrow -28x^2+30x^2=-40+40 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(5x^2+400=10x^2-5 \\ \Leftrightarrow 5x^2-10x^2=-5-400 \\ \Leftrightarrow -5x^2 = -405 \\ \Leftrightarrow x^2 = \frac{-405}{-5}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
5. \(2x^2-32=0 \\ \Leftrightarrow 2x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
6. \(3(2x^2-8)=-(-3x^2+699) \\ \Leftrightarrow 6x^2-24=3x^2-699 \\ \Leftrightarrow 6x^2-3x^2=-699+24 \\ \Leftrightarrow 3x^2 = -675 \\ \Leftrightarrow x^2 = \frac{-675}{3} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-3x^2+75=0 \\ \Leftrightarrow -3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{-3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
8. \(3(6x^2+2)=-(-20x^2+2) \\ \Leftrightarrow 18x^2+6=20x^2-2 \\ \Leftrightarrow 18x^2-20x^2=-2-6 \\ \Leftrightarrow -2x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
9. \(-8x^2+8=0 \\ \Leftrightarrow -8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
10. \(13x^2-1180=6x^2+3 \\ \Leftrightarrow 13x^2-6x^2=3+1180 \\ \Leftrightarrow 7x^2 = 1183 \\ \Leftrightarrow x^2 = \frac{1183}{7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
11. \(13x^2+291=5x^2+3 \\ \Leftrightarrow 13x^2-5x^2=3-291 \\ \Leftrightarrow 8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{8} < 0 \\ V = \varnothing \\ -----------------\)
12. \(4(-9x^2+4)=-(31x^2+304) \\ \Leftrightarrow -36x^2+16=-31x^2-304 \\ \Leftrightarrow -36x^2+31x^2=-304-16 \\ \Leftrightarrow -5x^2 = -320 \\ \Leftrightarrow x^2 = \frac{-320}{-5}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)