Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4(3x^2-5)=-(13x^2-19)\)
2. \(4(9x^2+9)=-(-38x^2+126)\)
3. \(8x^2+8=0\)
4. \(5(-4x^2+5)=-(25x^2+100)\)
5. \(x^2-16=0\)
6. \(6x^2+68=10x^2+4\)
7. \(-3x^2+112=-4x^2-9\)
8. \(-7x^2-252=0\)
9. \(-11x^2+1193=-4x^2+10\)
10. \(10x^2-385=8x^2+7\)
11. \(2(-3x^2-2)=-(4x^2+454)\)
12. \(16x^2-1354=10x^2-4\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4(3x^2-5)=-(13x^2-19) \\ \Leftrightarrow -12x^2+20=-13x^2+19 \\ \Leftrightarrow -12x^2+13x^2=19-20 \\ \Leftrightarrow x^2 = -1 \\ \Leftrightarrow x^2 = \frac{-1}{1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(4(9x^2+9)=-(-38x^2+126) \\ \Leftrightarrow 36x^2+36=38x^2-126 \\ \Leftrightarrow 36x^2-38x^2=-126-36 \\ \Leftrightarrow -2x^2 = -162 \\ \Leftrightarrow x^2 = \frac{-162}{-2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
3. \(8x^2+8=0 \\ \Leftrightarrow 8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{8} < 0 \\ V = \varnothing \\ -----------------\)
4. \(5(-4x^2+5)=-(25x^2+100) \\ \Leftrightarrow -20x^2+25=-25x^2-100 \\ \Leftrightarrow -20x^2+25x^2=-100-25 \\ \Leftrightarrow 5x^2 = -125 \\ \Leftrightarrow x^2 = \frac{-125}{5} < 0 \\ V = \varnothing \\ -----------------\)
5. \(x^2-16=0 \\ \Leftrightarrow x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{1}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
6. \(6x^2+68=10x^2+4 \\ \Leftrightarrow 6x^2-10x^2=4-68 \\ \Leftrightarrow -4x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
7. \(-3x^2+112=-4x^2-9 \\ \Leftrightarrow -3x^2+4x^2=-9-112 \\ \Leftrightarrow x^2 = -121 \\ \Leftrightarrow x^2 = \frac{-121}{1} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-7x^2-252=0 \\ \Leftrightarrow -7x^2 = 252 \\ \Leftrightarrow x^2 = \frac{252}{-7} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-11x^2+1193=-4x^2+10 \\ \Leftrightarrow -11x^2+4x^2=10-1193 \\ \Leftrightarrow -7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
10. \(10x^2-385=8x^2+7 \\ \Leftrightarrow 10x^2-8x^2=7+385 \\ \Leftrightarrow 2x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{2}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
11. \(2(-3x^2-2)=-(4x^2+454) \\ \Leftrightarrow -6x^2-4=-4x^2-454 \\ \Leftrightarrow -6x^2+4x^2=-454+4 \\ \Leftrightarrow -2x^2 = -450 \\ \Leftrightarrow x^2 = \frac{-450}{-2}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
12. \(16x^2-1354=10x^2-4 \\ \Leftrightarrow 16x^2-10x^2=-4+1354 \\ \Leftrightarrow 6x^2 = 1350 \\ \Leftrightarrow x^2 = \frac{1350}{6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)