Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3x^2-588=0\)
2. \(-6x^2-864=0\)
3. \(-5x^2+45=0\)
4. \(x^2+16=0\)
5. \(-4x^2-196=0\)
6. \(6x^2-150=0\)
7. \(-4(-3x^2+2)=-(-13x^2+108)\)
8. \(-9x^2-39=-8x^2+10\)
9. \(5(-10x^2-3)=-(42x^2-273)\)
10. \(-8x^2-512=0\)
11. \(6x^2-54=0\)
12. \(2(7x^2-7)=-(-8x^2-1336)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3x^2-588=0 \\ \Leftrightarrow -3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{-3} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-6x^2-864=0 \\ \Leftrightarrow -6x^2 = 864 \\ \Leftrightarrow x^2 = \frac{864}{-6} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-5x^2+45=0 \\ \Leftrightarrow -5x^2 = -45 \\ \Leftrightarrow x^2 = \frac{-45}{-5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
4. \(x^2+16=0 \\ \Leftrightarrow x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{1} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-4x^2-196=0 \\ \Leftrightarrow -4x^2 = 196 \\ \Leftrightarrow x^2 = \frac{196}{-4} < 0 \\ V = \varnothing \\ -----------------\)
6. \(6x^2-150=0 \\ \Leftrightarrow 6x^2 = 150 \\ \Leftrightarrow x^2 = \frac{150}{6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
7. \(-4(-3x^2+2)=-(-13x^2+108) \\ \Leftrightarrow 12x^2-8=13x^2-108 \\ \Leftrightarrow 12x^2-13x^2=-108+8 \\ \Leftrightarrow -x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
8. \(-9x^2-39=-8x^2+10 \\ \Leftrightarrow -9x^2+8x^2=10+39 \\ \Leftrightarrow -x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{-1} < 0 \\ V = \varnothing \\ -----------------\)
9. \(5(-10x^2-3)=-(42x^2-273) \\ \Leftrightarrow -50x^2-15=-42x^2+273 \\ \Leftrightarrow -50x^2+42x^2=273+15 \\ \Leftrightarrow -8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{-8} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-8x^2-512=0 \\ \Leftrightarrow -8x^2 = 512 \\ \Leftrightarrow x^2 = \frac{512}{-8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(6x^2-54=0 \\ \Leftrightarrow 6x^2 = 54 \\ \Leftrightarrow x^2 = \frac{54}{6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
12. \(2(7x^2-7)=-(-8x^2-1336) \\ \Leftrightarrow 14x^2-14=8x^2+1336 \\ \Leftrightarrow 14x^2-8x^2=1336+14 \\ \Leftrightarrow 6x^2 = 1350 \\ \Leftrightarrow x^2 = \frac{1350}{6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)