Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(10x^2-5)=-(-35x^2+20)\)
2. \(5(9x^2-7)=-(-40x^2-145)\)
3. \(-4(-6x^2-5)=-(-26x^2-22)\)
4. \(x^2+64=0\)
5. \(-x^2+196=0\)
6. \(14x^2+9=10x^2+9\)
7. \(-5x^2-330=-3x^2+8\)
8. \(-3(7x^2+6)=-(24x^2-90)\)
9. \(x^2+209=3x^2+9\)
10. \(-2(-3x^2+5)=-(0x^2-1340)\)
11. \(-4x^2+144=0\)
12. \(5x^2-20=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(10x^2-5)=-(-35x^2+20) \\ \Leftrightarrow 40x^2-20=35x^2-20 \\ \Leftrightarrow 40x^2-35x^2=-20+20 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(5(9x^2-7)=-(-40x^2-145) \\ \Leftrightarrow 45x^2-35=40x^2+145 \\ \Leftrightarrow 45x^2-40x^2=145+35 \\ \Leftrightarrow 5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
3. \(-4(-6x^2-5)=-(-26x^2-22) \\ \Leftrightarrow 24x^2+20=26x^2+22 \\ \Leftrightarrow 24x^2-26x^2=22-20 \\ \Leftrightarrow -2x^2 = 2 \\ \Leftrightarrow x^2 = \frac{2}{-2} < 0 \\ V = \varnothing \\ -----------------\)
4. \(x^2+64=0 \\ \Leftrightarrow x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{1} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-x^2+196=0 \\ \Leftrightarrow -x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
6. \(14x^2+9=10x^2+9 \\ \Leftrightarrow 14x^2-10x^2=9-9 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-5x^2-330=-3x^2+8 \\ \Leftrightarrow -5x^2+3x^2=8+330 \\ \Leftrightarrow -2x^2 = 338 \\ \Leftrightarrow x^2 = \frac{338}{-2} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-3(7x^2+6)=-(24x^2-90) \\ \Leftrightarrow -21x^2-18=-24x^2+90 \\ \Leftrightarrow -21x^2+24x^2=90+18 \\ \Leftrightarrow 3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{3}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
9. \(x^2+209=3x^2+9 \\ \Leftrightarrow x^2-3x^2=9-209 \\ \Leftrightarrow -2x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-2}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
10. \(-2(-3x^2+5)=-(0x^2-1340) \\ \Leftrightarrow 6x^2-10=0x^2+1340 \\ \Leftrightarrow 6x^2+0x^2=1340+10 \\ \Leftrightarrow 6x^2 = 1350 \\ \Leftrightarrow x^2 = \frac{1350}{6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
11. \(-4x^2+144=0 \\ \Leftrightarrow -4x^2 = -144 \\ \Leftrightarrow x^2 = \frac{-144}{-4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
12. \(5x^2-20=0 \\ \Leftrightarrow 5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)