Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2+1347=4x^2-5\)
2. \(3(3x^2-5)=-(-2x^2-13)\)
3. \(4(-10x^2+5)=-(33x^2+92)\)
4. \(-4(-9x^2+5)=-(-31x^2-825)\)
5. \(8x^2+1568=0\)
6. \(5x^2-500=0\)
7. \(3x^2-3=6x^2-3\)
8. \(-4x^2+0=0\)
9. \(x^2+333=-6x^2-10\)
10. \(4(-4x^2+6)=-(18x^2-74)\)
11. \(4(8x^2-9)=-(-31x^2+205)\)
12. \(-x^2+144=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2+1347=4x^2-5 \\ \Leftrightarrow -4x^2-4x^2=-5-1347 \\ \Leftrightarrow -8x^2 = -1352 \\ \Leftrightarrow x^2 = \frac{-1352}{-8}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
2. \(3(3x^2-5)=-(-2x^2-13) \\ \Leftrightarrow 9x^2-15=2x^2+13 \\ \Leftrightarrow 9x^2-2x^2=13+15 \\ \Leftrightarrow 7x^2 = 28 \\ \Leftrightarrow x^2 = \frac{28}{7}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
3. \(4(-10x^2+5)=-(33x^2+92) \\ \Leftrightarrow -40x^2+20=-33x^2-92 \\ \Leftrightarrow -40x^2+33x^2=-92-20 \\ \Leftrightarrow -7x^2 = -112 \\ \Leftrightarrow x^2 = \frac{-112}{-7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
4. \(-4(-9x^2+5)=-(-31x^2-825) \\ \Leftrightarrow 36x^2-20=31x^2+825 \\ \Leftrightarrow 36x^2-31x^2=825+20 \\ \Leftrightarrow 5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
5. \(8x^2+1568=0 \\ \Leftrightarrow 8x^2 = -1568 \\ \Leftrightarrow x^2 = \frac{-1568}{8} < 0 \\ V = \varnothing \\ -----------------\)
6. \(5x^2-500=0 \\ \Leftrightarrow 5x^2 = 500 \\ \Leftrightarrow x^2 = \frac{500}{5}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
7. \(3x^2-3=6x^2-3 \\ \Leftrightarrow 3x^2-6x^2=-3+3 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(-4x^2+0=0 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(x^2+333=-6x^2-10 \\ \Leftrightarrow x^2+6x^2=-10-333 \\ \Leftrightarrow 7x^2 = -343 \\ \Leftrightarrow x^2 = \frac{-343}{7} < 0 \\ V = \varnothing \\ -----------------\)
10. \(4(-4x^2+6)=-(18x^2-74) \\ \Leftrightarrow -16x^2+24=-18x^2+74 \\ \Leftrightarrow -16x^2+18x^2=74-24 \\ \Leftrightarrow 2x^2 = 50 \\ \Leftrightarrow x^2 = \frac{50}{2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
11. \(4(8x^2-9)=-(-31x^2+205) \\ \Leftrightarrow 32x^2-36=31x^2-205 \\ \Leftrightarrow 32x^2-31x^2=-205+36 \\ \Leftrightarrow x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{1} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-x^2+144=0 \\ \Leftrightarrow -x^2 = -144 \\ \Leftrightarrow x^2 = \frac{-144}{-1}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)