Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(-7x^2+9)=-(18x^2-34)\)
2. \(2(-3x^2+9)=-(4x^2-410)\)
3. \(-x^2+64=0\)
4. \(-5(-10x^2+6)=-(-48x^2+128)\)
5. \(5(5x^2-2)=-(-19x^2+610)\)
6. \(17x^2+65=9x^2-7\)
7. \(-7x^2+567=0\)
8. \(-2x^2-33=-6x^2+3\)
9. \(-5(9x^2+9)=-(37x^2-923)\)
10. \(-4x^2+35=-7x^2+8\)
11. \(-5x^2+0=0\)
12. \(-13x^2+966=-5x^2-2\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(-7x^2+9)=-(18x^2-34) \\ \Leftrightarrow -14x^2+18=-18x^2+34 \\ \Leftrightarrow -14x^2+18x^2=34-18 \\ \Leftrightarrow 4x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{4}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
2. \(2(-3x^2+9)=-(4x^2-410) \\ \Leftrightarrow -6x^2+18=-4x^2+410 \\ \Leftrightarrow -6x^2+4x^2=410-18 \\ \Leftrightarrow -2x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{-2} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-x^2+64=0 \\ \Leftrightarrow -x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-1}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
4. \(-5(-10x^2+6)=-(-48x^2+128) \\ \Leftrightarrow 50x^2-30=48x^2-128 \\ \Leftrightarrow 50x^2-48x^2=-128+30 \\ \Leftrightarrow 2x^2 = -98 \\ \Leftrightarrow x^2 = \frac{-98}{2} < 0 \\ V = \varnothing \\ -----------------\)
5. \(5(5x^2-2)=-(-19x^2+610) \\ \Leftrightarrow 25x^2-10=19x^2-610 \\ \Leftrightarrow 25x^2-19x^2=-610+10 \\ \Leftrightarrow 6x^2 = -600 \\ \Leftrightarrow x^2 = \frac{-600}{6} < 0 \\ V = \varnothing \\ -----------------\)
6. \(17x^2+65=9x^2-7 \\ \Leftrightarrow 17x^2-9x^2=-7-65 \\ \Leftrightarrow 8x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{8} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-7x^2+567=0 \\ \Leftrightarrow -7x^2 = -567 \\ \Leftrightarrow x^2 = \frac{-567}{-7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
8. \(-2x^2-33=-6x^2+3 \\ \Leftrightarrow -2x^2+6x^2=3+33 \\ \Leftrightarrow 4x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
9. \(-5(9x^2+9)=-(37x^2-923) \\ \Leftrightarrow -45x^2-45=-37x^2+923 \\ \Leftrightarrow -45x^2+37x^2=923+45 \\ \Leftrightarrow -8x^2 = 968 \\ \Leftrightarrow x^2 = \frac{968}{-8} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-4x^2+35=-7x^2+8 \\ \Leftrightarrow -4x^2+7x^2=8-35 \\ \Leftrightarrow 3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{3} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-5x^2+0=0 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-13x^2+966=-5x^2-2 \\ \Leftrightarrow -13x^2+5x^2=-2-966 \\ \Leftrightarrow -8x^2 = -968 \\ \Leftrightarrow x^2 = \frac{-968}{-8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)