Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2-597=-7x^2-9\)
2. \(2(3x^2-8)=-(-14x^2+1368)\)
3. \(-7x^2+700=0\)
4. \(4(-6x^2-2)=-(25x^2-17)\)
5. \(6x^2+295=9x^2-5\)
6. \(-2x^2+19=-5x^2-8\)
7. \(-3(2x^2+6)=-(x^2+23)\)
8. \(-10x^2-404=-6x^2-4\)
9. \(8x^2+968=0\)
10. \(-3x^2+4=-8x^2+4\)
11. \(-5(-4x^2+5)=-(-25x^2+525)\)
12. \(8x^2-512=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2-597=-7x^2-9 \\ \Leftrightarrow -4x^2+7x^2=-9+597 \\ \Leftrightarrow 3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
2. \(2(3x^2-8)=-(-14x^2+1368) \\ \Leftrightarrow 6x^2-16=14x^2-1368 \\ \Leftrightarrow 6x^2-14x^2=-1368+16 \\ \Leftrightarrow -8x^2 = -1352 \\ \Leftrightarrow x^2 = \frac{-1352}{-8}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
3. \(-7x^2+700=0 \\ \Leftrightarrow -7x^2 = -700 \\ \Leftrightarrow x^2 = \frac{-700}{-7}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
4. \(4(-6x^2-2)=-(25x^2-17) \\ \Leftrightarrow -24x^2-8=-25x^2+17 \\ \Leftrightarrow -24x^2+25x^2=17+8 \\ \Leftrightarrow x^2 = 25 \\ \Leftrightarrow x^2 = \frac{25}{1}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(6x^2+295=9x^2-5 \\ \Leftrightarrow 6x^2-9x^2=-5-295 \\ \Leftrightarrow -3x^2 = -300 \\ \Leftrightarrow x^2 = \frac{-300}{-3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
6. \(-2x^2+19=-5x^2-8 \\ \Leftrightarrow -2x^2+5x^2=-8-19 \\ \Leftrightarrow 3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{3} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-3(2x^2+6)=-(x^2+23) \\ \Leftrightarrow -6x^2-18=-x^2-23 \\ \Leftrightarrow -6x^2+x^2=-23+18 \\ \Leftrightarrow -5x^2 = -5 \\ \Leftrightarrow x^2 = \frac{-5}{-5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
8. \(-10x^2-404=-6x^2-4 \\ \Leftrightarrow -10x^2+6x^2=-4+404 \\ \Leftrightarrow -4x^2 = 400 \\ \Leftrightarrow x^2 = \frac{400}{-4} < 0 \\ V = \varnothing \\ -----------------\)
9. \(8x^2+968=0 \\ \Leftrightarrow 8x^2 = -968 \\ \Leftrightarrow x^2 = \frac{-968}{8} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-3x^2+4=-8x^2+4 \\ \Leftrightarrow -3x^2+8x^2=4-4 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-5(-4x^2+5)=-(-25x^2+525) \\ \Leftrightarrow 20x^2-25=25x^2-525 \\ \Leftrightarrow 20x^2-25x^2=-525+25 \\ \Leftrightarrow -5x^2 = -500 \\ \Leftrightarrow x^2 = \frac{-500}{-5}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
12. \(8x^2-512=0 \\ \Leftrightarrow 8x^2 = 512 \\ \Leftrightarrow x^2 = \frac{512}{8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)