Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(10x^2+171=9x^2+2\)
2. \(-3x^2+2=-2x^2-7\)
3. \(-5x^2-980=0\)
4. \(-3x^2+75=0\)
5. \(-3(5x^2+5)=-(12x^2+378)\)
6. \(-x^2-81=0\)
7. \(-3x^2-730=3x^2-4\)
8. \(-3x^2-12=0\)
9. \(2(-6x^2-9)=-(17x^2+143)\)
10. \(-2(7x^2+10)=-(6x^2+220)\)
11. \(5(-9x^2+3)=-(37x^2-15)\)
12. \(6x^2+600=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(10x^2+171=9x^2+2 \\ \Leftrightarrow 10x^2-9x^2=2-171 \\ \Leftrightarrow x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-3x^2+2=-2x^2-7 \\ \Leftrightarrow -3x^2+2x^2=-7-2 \\ \Leftrightarrow -x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{-1}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
3. \(-5x^2-980=0 \\ \Leftrightarrow -5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{-5} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-3x^2+75=0 \\ \Leftrightarrow -3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{-3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(-3(5x^2+5)=-(12x^2+378) \\ \Leftrightarrow -15x^2-15=-12x^2-378 \\ \Leftrightarrow -15x^2+12x^2=-378+15 \\ \Leftrightarrow -3x^2 = -363 \\ \Leftrightarrow x^2 = \frac{-363}{-3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
6. \(-x^2-81=0 \\ \Leftrightarrow -x^2 = 81 \\ \Leftrightarrow x^2 = \frac{81}{-1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-3x^2-730=3x^2-4 \\ \Leftrightarrow -3x^2-3x^2=-4+730 \\ \Leftrightarrow -6x^2 = 726 \\ \Leftrightarrow x^2 = \frac{726}{-6} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-3x^2-12=0 \\ \Leftrightarrow -3x^2 = 12 \\ \Leftrightarrow x^2 = \frac{12}{-3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(2(-6x^2-9)=-(17x^2+143) \\ \Leftrightarrow -12x^2-18=-17x^2-143 \\ \Leftrightarrow -12x^2+17x^2=-143+18 \\ \Leftrightarrow 5x^2 = -125 \\ \Leftrightarrow x^2 = \frac{-125}{5} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-2(7x^2+10)=-(6x^2+220) \\ \Leftrightarrow -14x^2-20=-6x^2-220 \\ \Leftrightarrow -14x^2+6x^2=-220+20 \\ \Leftrightarrow -8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
11. \(5(-9x^2+3)=-(37x^2-15) \\ \Leftrightarrow -45x^2+15=-37x^2+15 \\ \Leftrightarrow -45x^2+37x^2=15-15 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(6x^2+600=0 \\ \Leftrightarrow 6x^2 = -600 \\ \Leftrightarrow x^2 = \frac{-600}{6} < 0 \\ V = \varnothing \\ -----------------\)