Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(7x^2-489=3x^2-5\)
2. \(-x^2+225=0\)
3. \(4(-3x^2-2)=-(19x^2-1567)\)
4. \(-4(-4x^2+4)=-(-11x^2-4)\)
5. \(6x^2-24=0\)
6. \(2(10x^2-8)=-(-14x^2+40)\)
7. \(17x^2-9=10x^2-9\)
8. \(5(-3x^2-8)=-(14x^2+140)\)
9. \(x^2-4=0\)
10. \(7x^2-1008=0\)
11. \(5(4x^2-2)=-(-23x^2+10)\)
12. \(-5x^2+245=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(7x^2-489=3x^2-5 \\ \Leftrightarrow 7x^2-3x^2=-5+489 \\ \Leftrightarrow 4x^2 = 484 \\ \Leftrightarrow x^2 = \frac{484}{4}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
2. \(-x^2+225=0 \\ \Leftrightarrow -x^2 = -225 \\ \Leftrightarrow x^2 = \frac{-225}{-1}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
3. \(4(-3x^2-2)=-(19x^2-1567) \\ \Leftrightarrow -12x^2-8=-19x^2+1567 \\ \Leftrightarrow -12x^2+19x^2=1567+8 \\ \Leftrightarrow 7x^2 = 1575 \\ \Leftrightarrow x^2 = \frac{1575}{7}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
4. \(-4(-4x^2+4)=-(-11x^2-4) \\ \Leftrightarrow 16x^2-16=11x^2+4 \\ \Leftrightarrow 16x^2-11x^2=4+16 \\ \Leftrightarrow 5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
5. \(6x^2-24=0 \\ \Leftrightarrow 6x^2 = 24 \\ \Leftrightarrow x^2 = \frac{24}{6}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
6. \(2(10x^2-8)=-(-14x^2+40) \\ \Leftrightarrow 20x^2-16=14x^2-40 \\ \Leftrightarrow 20x^2-14x^2=-40+16 \\ \Leftrightarrow 6x^2 = -24 \\ \Leftrightarrow x^2 = \frac{-24}{6} < 0 \\ V = \varnothing \\ -----------------\)
7. \(17x^2-9=10x^2-9 \\ \Leftrightarrow 17x^2-10x^2=-9+9 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(5(-3x^2-8)=-(14x^2+140) \\ \Leftrightarrow -15x^2-40=-14x^2-140 \\ \Leftrightarrow -15x^2+14x^2=-140+40 \\ \Leftrightarrow -x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
9. \(x^2-4=0 \\ \Leftrightarrow x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{1}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
10. \(7x^2-1008=0 \\ \Leftrightarrow 7x^2 = 1008 \\ \Leftrightarrow x^2 = \frac{1008}{7}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
11. \(5(4x^2-2)=-(-23x^2+10) \\ \Leftrightarrow 20x^2-10=23x^2-10 \\ \Leftrightarrow 20x^2-23x^2=-10+10 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-5x^2+245=0 \\ \Leftrightarrow -5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{-5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)