Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(6x^2-10)=-(-37x^2+50)\)
2. \(-5(10x^2+4)=-(56x^2-34)\)
3. \(-2x^2-100=-4x^2-2\)
4. \(-6x^2+726=0\)
5. \(2(2x^2-8)=-(-9x^2+621)\)
6. \(5(-5x^2+4)=-(18x^2+92)\)
7. \(-14x^2+4=-10x^2+4\)
8. \(-5(8x^2+6)=-(39x^2+30)\)
9. \(5x^2-845=0\)
10. \(-2x^2+43=2x^2+7\)
11. \(-2(9x^2+8)=-(20x^2+34)\)
12. \(-3(4x^2-10)=-(19x^2-373)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(6x^2-10)=-(-37x^2+50) \\ \Leftrightarrow 30x^2-50=37x^2-50 \\ \Leftrightarrow 30x^2-37x^2=-50+50 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-5(10x^2+4)=-(56x^2-34) \\ \Leftrightarrow -50x^2-20=-56x^2+34 \\ \Leftrightarrow -50x^2+56x^2=34+20 \\ \Leftrightarrow 6x^2 = 54 \\ \Leftrightarrow x^2 = \frac{54}{6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
3. \(-2x^2-100=-4x^2-2 \\ \Leftrightarrow -2x^2+4x^2=-2+100 \\ \Leftrightarrow 2x^2 = 98 \\ \Leftrightarrow x^2 = \frac{98}{2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
4. \(-6x^2+726=0 \\ \Leftrightarrow -6x^2 = -726 \\ \Leftrightarrow x^2 = \frac{-726}{-6}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
5. \(2(2x^2-8)=-(-9x^2+621) \\ \Leftrightarrow 4x^2-16=9x^2-621 \\ \Leftrightarrow 4x^2-9x^2=-621+16 \\ \Leftrightarrow -5x^2 = -605 \\ \Leftrightarrow x^2 = \frac{-605}{-5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
6. \(5(-5x^2+4)=-(18x^2+92) \\ \Leftrightarrow -25x^2+20=-18x^2-92 \\ \Leftrightarrow -25x^2+18x^2=-92-20 \\ \Leftrightarrow -7x^2 = -112 \\ \Leftrightarrow x^2 = \frac{-112}{-7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
7. \(-14x^2+4=-10x^2+4 \\ \Leftrightarrow -14x^2+10x^2=4-4 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(-5(8x^2+6)=-(39x^2+30) \\ \Leftrightarrow -40x^2-30=-39x^2-30 \\ \Leftrightarrow -40x^2+39x^2=-30+30 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(5x^2-845=0 \\ \Leftrightarrow 5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
10. \(-2x^2+43=2x^2+7 \\ \Leftrightarrow -2x^2-2x^2=7-43 \\ \Leftrightarrow -4x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
11. \(-2(9x^2+8)=-(20x^2+34) \\ \Leftrightarrow -18x^2-16=-20x^2-34 \\ \Leftrightarrow -18x^2+20x^2=-34+16 \\ \Leftrightarrow 2x^2 = -18 \\ \Leftrightarrow x^2 = \frac{-18}{2} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-3(4x^2-10)=-(19x^2-373) \\ \Leftrightarrow -12x^2+30=-19x^2+373 \\ \Leftrightarrow -12x^2+19x^2=373-30 \\ \Leftrightarrow 7x^2 = 343 \\ \Leftrightarrow x^2 = \frac{343}{7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)