Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-7x^2+23=-2x^2+3\)
2. \(12x^2+477=8x^2-7\)
3. \(3(-7x^2+10)=-(25x^2-706)\)
4. \(-11x^2+440=-8x^2+8\)
5. \(-2(-5x^2+5)=-(-8x^2-152)\)
6. \(-5(8x^2+7)=-(44x^2+711)\)
7. \(13x^2-407=8x^2-2\)
8. \(-2x^2-795=-10x^2+5\)
9. \(-2x^2+162=0\)
10. \(-4(6x^2+6)=-(21x^2-276)\)
11. \(-8x^2+72=0\)
12. \(-x^2-100=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-7x^2+23=-2x^2+3 \\ \Leftrightarrow -7x^2+2x^2=3-23 \\ \Leftrightarrow -5x^2 = -20 \\ \Leftrightarrow x^2 = \frac{-20}{-5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
2. \(12x^2+477=8x^2-7 \\ \Leftrightarrow 12x^2-8x^2=-7-477 \\ \Leftrightarrow 4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{4} < 0 \\ V = \varnothing \\ -----------------\)
3. \(3(-7x^2+10)=-(25x^2-706) \\ \Leftrightarrow -21x^2+30=-25x^2+706 \\ \Leftrightarrow -21x^2+25x^2=706-30 \\ \Leftrightarrow 4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
4. \(-11x^2+440=-8x^2+8 \\ \Leftrightarrow -11x^2+8x^2=8-440 \\ \Leftrightarrow -3x^2 = -432 \\ \Leftrightarrow x^2 = \frac{-432}{-3}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
5. \(-2(-5x^2+5)=-(-8x^2-152) \\ \Leftrightarrow 10x^2-10=8x^2+152 \\ \Leftrightarrow 10x^2-8x^2=152+10 \\ \Leftrightarrow 2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
6. \(-5(8x^2+7)=-(44x^2+711) \\ \Leftrightarrow -40x^2-35=-44x^2-711 \\ \Leftrightarrow -40x^2+44x^2=-711+35 \\ \Leftrightarrow 4x^2 = -676 \\ \Leftrightarrow x^2 = \frac{-676}{4} < 0 \\ V = \varnothing \\ -----------------\)
7. \(13x^2-407=8x^2-2 \\ \Leftrightarrow 13x^2-8x^2=-2+407 \\ \Leftrightarrow 5x^2 = 405 \\ \Leftrightarrow x^2 = \frac{405}{5}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
8. \(-2x^2-795=-10x^2+5 \\ \Leftrightarrow -2x^2+10x^2=5+795 \\ \Leftrightarrow 8x^2 = 800 \\ \Leftrightarrow x^2 = \frac{800}{8}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
9. \(-2x^2+162=0 \\ \Leftrightarrow -2x^2 = -162 \\ \Leftrightarrow x^2 = \frac{-162}{-2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(-4(6x^2+6)=-(21x^2-276) \\ \Leftrightarrow -24x^2-24=-21x^2+276 \\ \Leftrightarrow -24x^2+21x^2=276+24 \\ \Leftrightarrow -3x^2 = 300 \\ \Leftrightarrow x^2 = \frac{300}{-3} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-8x^2+72=0 \\ \Leftrightarrow -8x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-8}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
12. \(-x^2-100=0 \\ \Leftrightarrow -x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{-1} < 0 \\ V = \varnothing \\ -----------------\)