Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2+0=0\)
2. \(-4(-8x^2+6)=-(-31x^2+33)\)
3. \(4(-7x^2-5)=-(25x^2+20)\)
4. \(4x^2+0=0\)
5. \(4x^2+29=6x^2-3\)
6. \(-3x^2+147=0\)
7. \(12x^2-493=7x^2+7\)
8. \(-9x^2-14=-5x^2+2\)
9. \(6x^2-294=0\)
10. \(-5(2x^2-10)=-(3x^2-22)\)
11. \(2(-5x^2+8)=-(16x^2-1366)\)
12. \(-x^2-1012=-7x^2+2\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2+0=0 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-4(-8x^2+6)=-(-31x^2+33) \\ \Leftrightarrow 32x^2-24=31x^2-33 \\ \Leftrightarrow 32x^2-31x^2=-33+24 \\ \Leftrightarrow x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{1} < 0 \\ V = \varnothing \\ -----------------\)
3. \(4(-7x^2-5)=-(25x^2+20) \\ \Leftrightarrow -28x^2-20=-25x^2-20 \\ \Leftrightarrow -28x^2+25x^2=-20+20 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(4x^2+0=0 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(4x^2+29=6x^2-3 \\ \Leftrightarrow 4x^2-6x^2=-3-29 \\ \Leftrightarrow -2x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{-2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
6. \(-3x^2+147=0 \\ \Leftrightarrow -3x^2 = -147 \\ \Leftrightarrow x^2 = \frac{-147}{-3}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
7. \(12x^2-493=7x^2+7 \\ \Leftrightarrow 12x^2-7x^2=7+493 \\ \Leftrightarrow 5x^2 = 500 \\ \Leftrightarrow x^2 = \frac{500}{5}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
8. \(-9x^2-14=-5x^2+2 \\ \Leftrightarrow -9x^2+5x^2=2+14 \\ \Leftrightarrow -4x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{-4} < 0 \\ V = \varnothing \\ -----------------\)
9. \(6x^2-294=0 \\ \Leftrightarrow 6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
10. \(-5(2x^2-10)=-(3x^2-22) \\ \Leftrightarrow -10x^2+50=-3x^2+22 \\ \Leftrightarrow -10x^2+3x^2=22-50 \\ \Leftrightarrow -7x^2 = -28 \\ \Leftrightarrow x^2 = \frac{-28}{-7}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
11. \(2(-5x^2+8)=-(16x^2-1366) \\ \Leftrightarrow -10x^2+16=-16x^2+1366 \\ \Leftrightarrow -10x^2+16x^2=1366-16 \\ \Leftrightarrow 6x^2 = 1350 \\ \Leftrightarrow x^2 = \frac{1350}{6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
12. \(-x^2-1012=-7x^2+2 \\ \Leftrightarrow -x^2+7x^2=2+1012 \\ \Leftrightarrow 6x^2 = 1014 \\ \Leftrightarrow x^2 = \frac{1014}{6}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)