Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2+484=0\)
2. \(-3x^2+675=0\)
3. \(4(-5x^2-2)=-(18x^2+136)\)
4. \(-6x^2+1176=0\)
5. \(-4(4x^2-8)=-(21x^2+373)\)
6. \(2(9x^2-7)=-(-12x^2-280)\)
7. \(-5x^2-726=-10x^2-6\)
8. \(4x^2-115=3x^2+6\)
9. \(-4x^2+1572=4x^2+4\)
10. \(x^2-315=-3x^2+9\)
11. \(-8x^2-288=0\)
12. \(-5x^2-980=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2+484=0 \\ \Leftrightarrow 4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{4} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-3x^2+675=0 \\ \Leftrightarrow -3x^2 = -675 \\ \Leftrightarrow x^2 = \frac{-675}{-3}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
3. \(4(-5x^2-2)=-(18x^2+136) \\ \Leftrightarrow -20x^2-8=-18x^2-136 \\ \Leftrightarrow -20x^2+18x^2=-136+8 \\ \Leftrightarrow -2x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
4. \(-6x^2+1176=0 \\ \Leftrightarrow -6x^2 = -1176 \\ \Leftrightarrow x^2 = \frac{-1176}{-6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
5. \(-4(4x^2-8)=-(21x^2+373) \\ \Leftrightarrow -16x^2+32=-21x^2-373 \\ \Leftrightarrow -16x^2+21x^2=-373-32 \\ \Leftrightarrow 5x^2 = -405 \\ \Leftrightarrow x^2 = \frac{-405}{5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(2(9x^2-7)=-(-12x^2-280) \\ \Leftrightarrow 18x^2-14=12x^2+280 \\ \Leftrightarrow 18x^2-12x^2=280+14 \\ \Leftrightarrow 6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
7. \(-5x^2-726=-10x^2-6 \\ \Leftrightarrow -5x^2+10x^2=-6+726 \\ \Leftrightarrow 5x^2 = 720 \\ \Leftrightarrow x^2 = \frac{720}{5}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
8. \(4x^2-115=3x^2+6 \\ \Leftrightarrow 4x^2-3x^2=6+115 \\ \Leftrightarrow x^2 = 121 \\ \Leftrightarrow x^2 = \frac{121}{1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(-4x^2+1572=4x^2+4 \\ \Leftrightarrow -4x^2-4x^2=4-1572 \\ \Leftrightarrow -8x^2 = -1568 \\ \Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
10. \(x^2-315=-3x^2+9 \\ \Leftrightarrow x^2+3x^2=9+315 \\ \Leftrightarrow 4x^2 = 324 \\ \Leftrightarrow x^2 = \frac{324}{4}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
11. \(-8x^2-288=0 \\ \Leftrightarrow -8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{-8} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-5x^2-980=0 \\ \Leftrightarrow -5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{-5} < 0 \\ V = \varnothing \\ -----------------\)