Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(5x^2+3)=-(32x^2-97)\)
2. \(5(-4x^2+5)=-(25x^2+100)\)
3. \(-2x^2+0=0\)
4. \(5(-8x^2+5)=-(34x^2+269)\)
5. \(3x^2+296=-5x^2+8\)
6. \(7x^2-252=2x^2-7\)
7. \(6x^2+0=0\)
8. \(-3(4x^2+7)=-(9x^2-567)\)
9. \(5x^2+353=2x^2-10\)
10. \(-12x^2+355=-9x^2-8\)
11. \(-5(2x^2+9)=-(11x^2+41)\)
12. \(6x^2+864=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(5x^2+3)=-(32x^2-97) \\ \Leftrightarrow -25x^2-15=-32x^2+97 \\ \Leftrightarrow -25x^2+32x^2=97+15 \\ \Leftrightarrow 7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
2. \(5(-4x^2+5)=-(25x^2+100) \\ \Leftrightarrow -20x^2+25=-25x^2-100 \\ \Leftrightarrow -20x^2+25x^2=-100-25 \\ \Leftrightarrow 5x^2 = -125 \\ \Leftrightarrow x^2 = \frac{-125}{5} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-2x^2+0=0 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(5(-8x^2+5)=-(34x^2+269) \\ \Leftrightarrow -40x^2+25=-34x^2-269 \\ \Leftrightarrow -40x^2+34x^2=-269-25 \\ \Leftrightarrow -6x^2 = -294 \\ \Leftrightarrow x^2 = \frac{-294}{-6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
5. \(3x^2+296=-5x^2+8 \\ \Leftrightarrow 3x^2+5x^2=8-296 \\ \Leftrightarrow 8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{8} < 0 \\ V = \varnothing \\ -----------------\)
6. \(7x^2-252=2x^2-7 \\ \Leftrightarrow 7x^2-2x^2=-7+252 \\ \Leftrightarrow 5x^2 = 245 \\ \Leftrightarrow x^2 = \frac{245}{5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
7. \(6x^2+0=0 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(-3(4x^2+7)=-(9x^2-567) \\ \Leftrightarrow -12x^2-21=-9x^2+567 \\ \Leftrightarrow -12x^2+9x^2=567+21 \\ \Leftrightarrow -3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{-3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(5x^2+353=2x^2-10 \\ \Leftrightarrow 5x^2-2x^2=-10-353 \\ \Leftrightarrow 3x^2 = -363 \\ \Leftrightarrow x^2 = \frac{-363}{3} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-12x^2+355=-9x^2-8 \\ \Leftrightarrow -12x^2+9x^2=-8-355 \\ \Leftrightarrow -3x^2 = -363 \\ \Leftrightarrow x^2 = \frac{-363}{-3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
11. \(-5(2x^2+9)=-(11x^2+41) \\ \Leftrightarrow -10x^2-45=-11x^2-41 \\ \Leftrightarrow -10x^2+11x^2=-41+45 \\ \Leftrightarrow x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{1}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(6x^2+864=0 \\ \Leftrightarrow 6x^2 = -864 \\ \Leftrightarrow x^2 = \frac{-864}{6} < 0 \\ V = \varnothing \\ -----------------\)