Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(5x^2-5)=-(22x^2-22)\)
2. \(10x^2-842=3x^2+5\)
3. \(-2x^2-8=0\)
4. \(2x^2+338=0\)
5. \(3(8x^2+4)=-(-18x^2-876)\)
6. \(x^2-169=0\)
7. \(-4x^2+900=0\)
8. \(-5(3x^2-4)=-(19x^2-920)\)
9. \(-15x^2-7=-8x^2-7\)
10. \(-5x^2-209=-7x^2-9\)
11. \(-5(4x^2-10)=-(14x^2+46)\)
12. \(-4(7x^2-9)=-(33x^2+209)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(5x^2-5)=-(22x^2-22) \\ \Leftrightarrow -25x^2+25=-22x^2+22 \\ \Leftrightarrow -25x^2+22x^2=22-25 \\ \Leftrightarrow -3x^2 = -3 \\ \Leftrightarrow x^2 = \frac{-3}{-3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
2. \(10x^2-842=3x^2+5 \\ \Leftrightarrow 10x^2-3x^2=5+842 \\ \Leftrightarrow 7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
3. \(-2x^2-8=0 \\ \Leftrightarrow -2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{-2} < 0 \\ V = \varnothing \\ -----------------\)
4. \(2x^2+338=0 \\ \Leftrightarrow 2x^2 = -338 \\ \Leftrightarrow x^2 = \frac{-338}{2} < 0 \\ V = \varnothing \\ -----------------\)
5. \(3(8x^2+4)=-(-18x^2-876) \\ \Leftrightarrow 24x^2+12=18x^2+876 \\ \Leftrightarrow 24x^2-18x^2=876-12 \\ \Leftrightarrow 6x^2 = 864 \\ \Leftrightarrow x^2 = \frac{864}{6}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
6. \(x^2-169=0 \\ \Leftrightarrow x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
7. \(-4x^2+900=0 \\ \Leftrightarrow -4x^2 = -900 \\ \Leftrightarrow x^2 = \frac{-900}{-4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
8. \(-5(3x^2-4)=-(19x^2-920) \\ \Leftrightarrow -15x^2+20=-19x^2+920 \\ \Leftrightarrow -15x^2+19x^2=920-20 \\ \Leftrightarrow 4x^2 = 900 \\ \Leftrightarrow x^2 = \frac{900}{4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
9. \(-15x^2-7=-8x^2-7 \\ \Leftrightarrow -15x^2+8x^2=-7+7 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(-5x^2-209=-7x^2-9 \\ \Leftrightarrow -5x^2+7x^2=-9+209 \\ \Leftrightarrow 2x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{2}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
11. \(-5(4x^2-10)=-(14x^2+46) \\ \Leftrightarrow -20x^2+50=-14x^2-46 \\ \Leftrightarrow -20x^2+14x^2=-46-50 \\ \Leftrightarrow -6x^2 = -96 \\ \Leftrightarrow x^2 = \frac{-96}{-6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
12. \(-4(7x^2-9)=-(33x^2+209) \\ \Leftrightarrow -28x^2+36=-33x^2-209 \\ \Leftrightarrow -28x^2+33x^2=-209-36 \\ \Leftrightarrow 5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{5} < 0 \\ V = \varnothing \\ -----------------\)