Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(12x^2+586=8x^2+10\)
2. \(5x^2-10=9x^2-10\)
3. \(8x^2+23=10x^2+5\)
4. \(9x^2+238=7x^2-4\)
5. \(-7x^2+1372=0\)
6. \(-6x^2-96=0\)
7. \(4(-4x^2-3)=-(14x^2+300)\)
8. \(2(-2x^2-3)=-(12x^2+654)\)
9. \(-4x^2-324=0\)
10. \(-10x^2-209=-4x^2+7\)
11. \(-2x^2+2=0\)
12. \(3x^2-258=-4x^2-6\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(12x^2+586=8x^2+10 \\ \Leftrightarrow 12x^2-8x^2=10-586 \\ \Leftrightarrow 4x^2 = -576 \\ \Leftrightarrow x^2 = \frac{-576}{4} < 0 \\ V = \varnothing \\ -----------------\)
2. \(5x^2-10=9x^2-10 \\ \Leftrightarrow 5x^2-9x^2=-10+10 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(8x^2+23=10x^2+5 \\ \Leftrightarrow 8x^2-10x^2=5-23 \\ \Leftrightarrow -2x^2 = -18 \\ \Leftrightarrow x^2 = \frac{-18}{-2}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
4. \(9x^2+238=7x^2-4 \\ \Leftrightarrow 9x^2-7x^2=-4-238 \\ \Leftrightarrow 2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{2} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-7x^2+1372=0 \\ \Leftrightarrow -7x^2 = -1372 \\ \Leftrightarrow x^2 = \frac{-1372}{-7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
6. \(-6x^2-96=0 \\ \Leftrightarrow -6x^2 = 96 \\ \Leftrightarrow x^2 = \frac{96}{-6} < 0 \\ V = \varnothing \\ -----------------\)
7. \(4(-4x^2-3)=-(14x^2+300) \\ \Leftrightarrow -16x^2-12=-14x^2-300 \\ \Leftrightarrow -16x^2+14x^2=-300+12 \\ \Leftrightarrow -2x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-2}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
8. \(2(-2x^2-3)=-(12x^2+654) \\ \Leftrightarrow -4x^2-6=-12x^2-654 \\ \Leftrightarrow -4x^2+12x^2=-654+6 \\ \Leftrightarrow 8x^2 = -648 \\ \Leftrightarrow x^2 = \frac{-648}{8} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-4x^2-324=0 \\ \Leftrightarrow -4x^2 = 324 \\ \Leftrightarrow x^2 = \frac{324}{-4} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-10x^2-209=-4x^2+7 \\ \Leftrightarrow -10x^2+4x^2=7+209 \\ \Leftrightarrow -6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{-6} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-2x^2+2=0 \\ \Leftrightarrow -2x^2 = -2 \\ \Leftrightarrow x^2 = \frac{-2}{-2}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
12. \(3x^2-258=-4x^2-6 \\ \Leftrightarrow 3x^2+4x^2=-6+258 \\ \Leftrightarrow 7x^2 = 252 \\ \Leftrightarrow x^2 = \frac{252}{7}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)