Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(5x^2-5)=-(-22x^2-218)\)
2. \(4x^2+96=5x^2-4\)
3. \(-x^2-1=0\)
4. \(-5(-5x^2+4)=-(-22x^2+212)\)
5. \(x^2-196=0\)
6. \(-4(-6x^2+9)=-(-19x^2-209)\)
7. \(-3(10x^2-8)=-(33x^2-216)\)
8. \(-12x^2+1347=-4x^2-5\)
9. \(-13x^2+654=-5x^2+6\)
10. \(3(10x^2-9)=-(-28x^2-365)\)
11. \(4x^2-83=7x^2-8\)
12. \(-3(4x^2-5)=-(5x^2+13)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(5x^2-5)=-(-22x^2-218) \\ \Leftrightarrow 25x^2-25=22x^2+218 \\ \Leftrightarrow 25x^2-22x^2=218+25 \\ \Leftrightarrow 3x^2 = 243 \\ \Leftrightarrow x^2 = \frac{243}{3}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
2. \(4x^2+96=5x^2-4 \\ \Leftrightarrow 4x^2-5x^2=-4-96 \\ \Leftrightarrow -x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
3. \(-x^2-1=0 \\ \Leftrightarrow -x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{-1} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-5(-5x^2+4)=-(-22x^2+212) \\ \Leftrightarrow 25x^2-20=22x^2-212 \\ \Leftrightarrow 25x^2-22x^2=-212+20 \\ \Leftrightarrow 3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(x^2-196=0 \\ \Leftrightarrow x^2 = 196 \\ \Leftrightarrow x^2 = \frac{196}{1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
6. \(-4(-6x^2+9)=-(-19x^2-209) \\ \Leftrightarrow 24x^2-36=19x^2+209 \\ \Leftrightarrow 24x^2-19x^2=209+36 \\ \Leftrightarrow 5x^2 = 245 \\ \Leftrightarrow x^2 = \frac{245}{5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
7. \(-3(10x^2-8)=-(33x^2-216) \\ \Leftrightarrow -30x^2+24=-33x^2+216 \\ \Leftrightarrow -30x^2+33x^2=216-24 \\ \Leftrightarrow 3x^2 = 192 \\ \Leftrightarrow x^2 = \frac{192}{3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
8. \(-12x^2+1347=-4x^2-5 \\ \Leftrightarrow -12x^2+4x^2=-5-1347 \\ \Leftrightarrow -8x^2 = -1352 \\ \Leftrightarrow x^2 = \frac{-1352}{-8}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
9. \(-13x^2+654=-5x^2+6 \\ \Leftrightarrow -13x^2+5x^2=6-654 \\ \Leftrightarrow -8x^2 = -648 \\ \Leftrightarrow x^2 = \frac{-648}{-8}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(3(10x^2-9)=-(-28x^2-365) \\ \Leftrightarrow 30x^2-27=28x^2+365 \\ \Leftrightarrow 30x^2-28x^2=365+27 \\ \Leftrightarrow 2x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{2}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
11. \(4x^2-83=7x^2-8 \\ \Leftrightarrow 4x^2-7x^2=-8+83 \\ \Leftrightarrow -3x^2 = 75 \\ \Leftrightarrow x^2 = \frac{75}{-3} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-3(4x^2-5)=-(5x^2+13) \\ \Leftrightarrow -12x^2+15=-5x^2-13 \\ \Leftrightarrow -12x^2+5x^2=-13-15 \\ \Leftrightarrow -7x^2 = -28 \\ \Leftrightarrow x^2 = \frac{-28}{-7}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)