Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(4x^2-6)=-(4x^2+110)\)
2. \(5x^2+218=4x^2-7\)
3. \(2(-10x^2-2)=-(15x^2-1121)\)
4. \(-6x^2+6=0\)
5. \(-4(-10x^2+4)=-(-41x^2+25)\)
6. \(5x^2-245=0\)
7. \(-3x^2-243=0\)
8. \(-8x^2+0=0\)
9. \(-4(4x^2+8)=-(19x^2-268)\)
10. \(4(-5x^2-2)=-(28x^2+8)\)
11. \(2(-9x^2+8)=-(20x^2+2)\)
12. \(-x^2+25=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(4x^2-6)=-(4x^2+110) \\ \Leftrightarrow -12x^2+18=-4x^2-110 \\ \Leftrightarrow -12x^2+4x^2=-110-18 \\ \Leftrightarrow -8x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-8}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
2. \(5x^2+218=4x^2-7 \\ \Leftrightarrow 5x^2-4x^2=-7-218 \\ \Leftrightarrow x^2 = -225 \\ \Leftrightarrow x^2 = \frac{-225}{1} < 0 \\ V = \varnothing \\ -----------------\)
3. \(2(-10x^2-2)=-(15x^2-1121) \\ \Leftrightarrow -20x^2-4=-15x^2+1121 \\ \Leftrightarrow -20x^2+15x^2=1121+4 \\ \Leftrightarrow -5x^2 = 1125 \\ \Leftrightarrow x^2 = \frac{1125}{-5} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-6x^2+6=0 \\ \Leftrightarrow -6x^2 = -6 \\ \Leftrightarrow x^2 = \frac{-6}{-6}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
5. \(-4(-10x^2+4)=-(-41x^2+25) \\ \Leftrightarrow 40x^2-16=41x^2-25 \\ \Leftrightarrow 40x^2-41x^2=-25+16 \\ \Leftrightarrow -x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{-1}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
6. \(5x^2-245=0 \\ \Leftrightarrow 5x^2 = 245 \\ \Leftrightarrow x^2 = \frac{245}{5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
7. \(-3x^2-243=0 \\ \Leftrightarrow -3x^2 = 243 \\ \Leftrightarrow x^2 = \frac{243}{-3} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-8x^2+0=0 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(-4(4x^2+8)=-(19x^2-268) \\ \Leftrightarrow -16x^2-32=-19x^2+268 \\ \Leftrightarrow -16x^2+19x^2=268+32 \\ \Leftrightarrow 3x^2 = 300 \\ \Leftrightarrow x^2 = \frac{300}{3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
10. \(4(-5x^2-2)=-(28x^2+8) \\ \Leftrightarrow -20x^2-8=-28x^2-8 \\ \Leftrightarrow -20x^2+28x^2=-8+8 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(2(-9x^2+8)=-(20x^2+2) \\ \Leftrightarrow -18x^2+16=-20x^2-2 \\ \Leftrightarrow -18x^2+20x^2=-2-16 \\ \Leftrightarrow 2x^2 = -18 \\ \Leftrightarrow x^2 = \frac{-18}{2} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-x^2+25=0 \\ \Leftrightarrow -x^2 = -25 \\ \Leftrightarrow x^2 = \frac{-25}{-1}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)