Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2-8=0\)
2. \(-8x^2-288=0\)
3. \(-x^2-1=0\)
4. \(5(-8x^2+3)=-(47x^2+48)\)
5. \(-11x^2-29=-9x^2+3\)
6. \(-2x^2+0=0\)
7. \(-x^2+121=0\)
8. \(-4(3x^2+5)=-(16x^2-656)\)
9. \(-4x^2+8=-5x^2+8\)
10. \(5x^2+720=0\)
11. \(2(-9x^2+8)=-(20x^2-466)\)
12. \(3(-3x^2-2)=-(17x^2-1562)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2-8=0 \\ \Leftrightarrow -2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{-2} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-8x^2-288=0 \\ \Leftrightarrow -8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{-8} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-x^2-1=0 \\ \Leftrightarrow -x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{-1} < 0 \\ V = \varnothing \\ -----------------\)
4. \(5(-8x^2+3)=-(47x^2+48) \\ \Leftrightarrow -40x^2+15=-47x^2-48 \\ \Leftrightarrow -40x^2+47x^2=-48-15 \\ \Leftrightarrow 7x^2 = -63 \\ \Leftrightarrow x^2 = \frac{-63}{7} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-11x^2-29=-9x^2+3 \\ \Leftrightarrow -11x^2+9x^2=3+29 \\ \Leftrightarrow -2x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{-2} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-2x^2+0=0 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-x^2+121=0 \\ \Leftrightarrow -x^2 = -121 \\ \Leftrightarrow x^2 = \frac{-121}{-1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
8. \(-4(3x^2+5)=-(16x^2-656) \\ \Leftrightarrow -12x^2-20=-16x^2+656 \\ \Leftrightarrow -12x^2+16x^2=656+20 \\ \Leftrightarrow 4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
9. \(-4x^2+8=-5x^2+8 \\ \Leftrightarrow -4x^2+5x^2=8-8 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(5x^2+720=0 \\ \Leftrightarrow 5x^2 = -720 \\ \Leftrightarrow x^2 = \frac{-720}{5} < 0 \\ V = \varnothing \\ -----------------\)
11. \(2(-9x^2+8)=-(20x^2-466) \\ \Leftrightarrow -18x^2+16=-20x^2+466 \\ \Leftrightarrow -18x^2+20x^2=466-16 \\ \Leftrightarrow 2x^2 = 450 \\ \Leftrightarrow x^2 = \frac{450}{2}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
12. \(3(-3x^2-2)=-(17x^2-1562) \\ \Leftrightarrow -9x^2-6=-17x^2+1562 \\ \Leftrightarrow -9x^2+17x^2=1562+6 \\ \Leftrightarrow 8x^2 = 1568 \\ \Leftrightarrow x^2 = \frac{1568}{8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)