Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2+64=0\)
2. \(-4(2x^2+4)=-(2x^2+22)\)
3. \(4x^2-576=0\)
4. \(-5x^2-320=0\)
5. \(-5x^2-245=0\)
6. \(x^2-515=-2x^2-8\)
7. \(4(-9x^2-4)=-(43x^2-236)\)
8. \(-5x^2+5=0\)
9. \(11x^2+1=10x^2-8\)
10. \(8x^2+1352=0\)
11. \(-5x^2+20=0\)
12. \(x^2+679=5x^2+3\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2+64=0 \\ \Leftrightarrow -4x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
2. \(-4(2x^2+4)=-(2x^2+22) \\ \Leftrightarrow -8x^2-16=-2x^2-22 \\ \Leftrightarrow -8x^2+2x^2=-22+16 \\ \Leftrightarrow -6x^2 = -6 \\ \Leftrightarrow x^2 = \frac{-6}{-6}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
3. \(4x^2-576=0 \\ \Leftrightarrow 4x^2 = 576 \\ \Leftrightarrow x^2 = \frac{576}{4}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
4. \(-5x^2-320=0 \\ \Leftrightarrow -5x^2 = 320 \\ \Leftrightarrow x^2 = \frac{320}{-5} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-5x^2-245=0 \\ \Leftrightarrow -5x^2 = 245 \\ \Leftrightarrow x^2 = \frac{245}{-5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(x^2-515=-2x^2-8 \\ \Leftrightarrow x^2+2x^2=-8+515 \\ \Leftrightarrow 3x^2 = 507 \\ \Leftrightarrow x^2 = \frac{507}{3}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
7. \(4(-9x^2-4)=-(43x^2-236) \\ \Leftrightarrow -36x^2-16=-43x^2+236 \\ \Leftrightarrow -36x^2+43x^2=236+16 \\ \Leftrightarrow 7x^2 = 252 \\ \Leftrightarrow x^2 = \frac{252}{7}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
8. \(-5x^2+5=0 \\ \Leftrightarrow -5x^2 = -5 \\ \Leftrightarrow x^2 = \frac{-5}{-5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(11x^2+1=10x^2-8 \\ \Leftrightarrow 11x^2-10x^2=-8-1 \\ \Leftrightarrow x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{1} < 0 \\ V = \varnothing \\ -----------------\)
10. \(8x^2+1352=0 \\ \Leftrightarrow 8x^2 = -1352 \\ \Leftrightarrow x^2 = \frac{-1352}{8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-5x^2+20=0 \\ \Leftrightarrow -5x^2 = -20 \\ \Leftrightarrow x^2 = \frac{-20}{-5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(x^2+679=5x^2+3 \\ \Leftrightarrow x^2-5x^2=3-679 \\ \Leftrightarrow -4x^2 = -676 \\ \Leftrightarrow x^2 = \frac{-676}{-4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)