Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-9x^2+396=-4x^2-9\)
2. \(2x^2-338=0\)
3. \(-4x^2+256=0\)
4. \(-2x^2+128=3x^2+3\)
5. \(3(2x^2+4)=-(-14x^2-4)\)
6. \(2(2x^2-3)=-(3x^2-246)\)
7. \(-13x^2+674=-9x^2-2\)
8. \(-5x^2+845=0\)
9. \(-10x^2+160=-9x^2-9\)
10. \(-x^2+36=0\)
11. \(-12x^2+1366=-5x^2-6\)
12. \(-2(-10x^2-9)=-(-22x^2+432)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-9x^2+396=-4x^2-9 \\ \Leftrightarrow -9x^2+4x^2=-9-396 \\ \Leftrightarrow -5x^2 = -405 \\ \Leftrightarrow x^2 = \frac{-405}{-5}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
2. \(2x^2-338=0 \\ \Leftrightarrow 2x^2 = 338 \\ \Leftrightarrow x^2 = \frac{338}{2}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
3. \(-4x^2+256=0 \\ \Leftrightarrow -4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{-4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
4. \(-2x^2+128=3x^2+3 \\ \Leftrightarrow -2x^2-3x^2=3-128 \\ \Leftrightarrow -5x^2 = -125 \\ \Leftrightarrow x^2 = \frac{-125}{-5}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(3(2x^2+4)=-(-14x^2-4) \\ \Leftrightarrow 6x^2+12=14x^2+4 \\ \Leftrightarrow 6x^2-14x^2=4-12 \\ \Leftrightarrow -8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(2(2x^2-3)=-(3x^2-246) \\ \Leftrightarrow 4x^2-6=-3x^2+246 \\ \Leftrightarrow 4x^2+3x^2=246+6 \\ \Leftrightarrow 7x^2 = 252 \\ \Leftrightarrow x^2 = \frac{252}{7}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
7. \(-13x^2+674=-9x^2-2 \\ \Leftrightarrow -13x^2+9x^2=-2-674 \\ \Leftrightarrow -4x^2 = -676 \\ \Leftrightarrow x^2 = \frac{-676}{-4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
8. \(-5x^2+845=0 \\ \Leftrightarrow -5x^2 = -845 \\ \Leftrightarrow x^2 = \frac{-845}{-5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
9. \(-10x^2+160=-9x^2-9 \\ \Leftrightarrow -10x^2+9x^2=-9-160 \\ \Leftrightarrow -x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{-1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
10. \(-x^2+36=0 \\ \Leftrightarrow -x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-1}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
11. \(-12x^2+1366=-5x^2-6 \\ \Leftrightarrow -12x^2+5x^2=-6-1366 \\ \Leftrightarrow -7x^2 = -1372 \\ \Leftrightarrow x^2 = \frac{-1372}{-7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
12. \(-2(-10x^2-9)=-(-22x^2+432) \\ \Leftrightarrow 20x^2+18=22x^2-432 \\ \Leftrightarrow 20x^2-22x^2=-432-18 \\ \Leftrightarrow -2x^2 = -450 \\ \Leftrightarrow x^2 = \frac{-450}{-2}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)