Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2-144=0\)
2. \(x^2+300=7x^2+6\)
3. \(-7x^2+89=-2x^2+9\)
4. \(-3(8x^2+3)=-(20x^2+45)\)
5. \(-7x^2+11=-2x^2-9\)
6. \(3(-7x^2+7)=-(20x^2+175)\)
7. \(2x^2-8=0\)
8. \(3(2x^2-3)=-(-14x^2+81)\)
9. \(7x^2+15=8x^2+6\)
10. \(-x^2-503=4x^2-3\)
11. \(-5x^2-193=-3x^2+7\)
12. \(-8x^2+0=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2-144=0 \\ \Leftrightarrow 4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
2. \(x^2+300=7x^2+6 \\ \Leftrightarrow x^2-7x^2=6-300 \\ \Leftrightarrow -6x^2 = -294 \\ \Leftrightarrow x^2 = \frac{-294}{-6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
3. \(-7x^2+89=-2x^2+9 \\ \Leftrightarrow -7x^2+2x^2=9-89 \\ \Leftrightarrow -5x^2 = -80 \\ \Leftrightarrow x^2 = \frac{-80}{-5}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
4. \(-3(8x^2+3)=-(20x^2+45) \\ \Leftrightarrow -24x^2-9=-20x^2-45 \\ \Leftrightarrow -24x^2+20x^2=-45+9 \\ \Leftrightarrow -4x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
5. \(-7x^2+11=-2x^2-9 \\ \Leftrightarrow -7x^2+2x^2=-9-11 \\ \Leftrightarrow -5x^2 = -20 \\ \Leftrightarrow x^2 = \frac{-20}{-5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
6. \(3(-7x^2+7)=-(20x^2+175) \\ \Leftrightarrow -21x^2+21=-20x^2-175 \\ \Leftrightarrow -21x^2+20x^2=-175-21 \\ \Leftrightarrow -x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
7. \(2x^2-8=0 \\ \Leftrightarrow 2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
8. \(3(2x^2-3)=-(-14x^2+81) \\ \Leftrightarrow 6x^2-9=14x^2-81 \\ \Leftrightarrow 6x^2-14x^2=-81+9 \\ \Leftrightarrow -8x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-8}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
9. \(7x^2+15=8x^2+6 \\ \Leftrightarrow 7x^2-8x^2=6-15 \\ \Leftrightarrow -x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{-1}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
10. \(-x^2-503=4x^2-3 \\ \Leftrightarrow -x^2-4x^2=-3+503 \\ \Leftrightarrow -5x^2 = 500 \\ \Leftrightarrow x^2 = \frac{500}{-5} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-5x^2-193=-3x^2+7 \\ \Leftrightarrow -5x^2+3x^2=7+193 \\ \Leftrightarrow -2x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{-2} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-8x^2+0=0 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)