Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(9x^2-8)=-(34x^2-24)\)
2. \(4(-8x^2-2)=-(28x^2-392)\)
3. \(5(7x^2-6)=-(-37x^2+422)\)
4. \(5(-7x^2+3)=-(43x^2-303)\)
5. \(-3x^2-432=0\)
6. \(4(-3x^2-9)=-(17x^2-144)\)
7. \(5(5x^2-2)=-(-29x^2-474)\)
8. \(-4x^2-330=-8x^2-6\)
9. \(-4x^2+484=0\)
10. \(-6x^2+1014=0\)
11. \(5(-10x^2+2)=-(55x^2-855)\)
12. \(-x^2+100=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(9x^2-8)=-(34x^2-24) \\ \Leftrightarrow -27x^2+24=-34x^2+24 \\ \Leftrightarrow -27x^2+34x^2=24-24 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(4(-8x^2-2)=-(28x^2-392) \\ \Leftrightarrow -32x^2-8=-28x^2+392 \\ \Leftrightarrow -32x^2+28x^2=392+8 \\ \Leftrightarrow -4x^2 = 400 \\ \Leftrightarrow x^2 = \frac{400}{-4} < 0 \\ V = \varnothing \\ -----------------\)
3. \(5(7x^2-6)=-(-37x^2+422) \\ \Leftrightarrow 35x^2-30=37x^2-422 \\ \Leftrightarrow 35x^2-37x^2=-422+30 \\ \Leftrightarrow -2x^2 = -392 \\ \Leftrightarrow x^2 = \frac{-392}{-2}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
4. \(5(-7x^2+3)=-(43x^2-303) \\ \Leftrightarrow -35x^2+15=-43x^2+303 \\ \Leftrightarrow -35x^2+43x^2=303-15 \\ \Leftrightarrow 8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
5. \(-3x^2-432=0 \\ \Leftrightarrow -3x^2 = 432 \\ \Leftrightarrow x^2 = \frac{432}{-3} < 0 \\ V = \varnothing \\ -----------------\)
6. \(4(-3x^2-9)=-(17x^2-144) \\ \Leftrightarrow -12x^2-36=-17x^2+144 \\ \Leftrightarrow -12x^2+17x^2=144+36 \\ \Leftrightarrow 5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
7. \(5(5x^2-2)=-(-29x^2-474) \\ \Leftrightarrow 25x^2-10=29x^2+474 \\ \Leftrightarrow 25x^2-29x^2=474+10 \\ \Leftrightarrow -4x^2 = 484 \\ \Leftrightarrow x^2 = \frac{484}{-4} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-4x^2-330=-8x^2-6 \\ \Leftrightarrow -4x^2+8x^2=-6+330 \\ \Leftrightarrow 4x^2 = 324 \\ \Leftrightarrow x^2 = \frac{324}{4}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
9. \(-4x^2+484=0 \\ \Leftrightarrow -4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{-4}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
10. \(-6x^2+1014=0 \\ \Leftrightarrow -6x^2 = -1014 \\ \Leftrightarrow x^2 = \frac{-1014}{-6}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
11. \(5(-10x^2+2)=-(55x^2-855) \\ \Leftrightarrow -50x^2+10=-55x^2+855 \\ \Leftrightarrow -50x^2+55x^2=855-10 \\ \Leftrightarrow 5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
12. \(-x^2+100=0 \\ \Leftrightarrow -x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)