Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(17x^2-120=10x^2-8\)
2. \(-4(-6x^2+2)=-(-27x^2+440)\)
3. \(4x^2-900=0\)
4. \(2x^2-50=0\)
5. \(-2(-6x^2-3)=-(-11x^2-87)\)
6. \(-2(-10x^2-8)=-(-25x^2+164)\)
7. \(3(-10x^2-8)=-(28x^2+26)\)
8. \(x^2+153=3x^2-9\)
9. \(-7x^2+120=-5x^2-8\)
10. \(-x^2+31=-4x^2+4\)
11. \(2x^2-18=0\)
12. \(7x^2+28=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(17x^2-120=10x^2-8 \\ \Leftrightarrow 17x^2-10x^2=-8+120 \\ \Leftrightarrow 7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
2. \(-4(-6x^2+2)=-(-27x^2+440) \\ \Leftrightarrow 24x^2-8=27x^2-440 \\ \Leftrightarrow 24x^2-27x^2=-440+8 \\ \Leftrightarrow -3x^2 = -432 \\ \Leftrightarrow x^2 = \frac{-432}{-3}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
3. \(4x^2-900=0 \\ \Leftrightarrow 4x^2 = 900 \\ \Leftrightarrow x^2 = \frac{900}{4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
4. \(2x^2-50=0 \\ \Leftrightarrow 2x^2 = 50 \\ \Leftrightarrow x^2 = \frac{50}{2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(-2(-6x^2-3)=-(-11x^2-87) \\ \Leftrightarrow 12x^2+6=11x^2+87 \\ \Leftrightarrow 12x^2-11x^2=87-6 \\ \Leftrightarrow x^2 = 81 \\ \Leftrightarrow x^2 = \frac{81}{1}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
6. \(-2(-10x^2-8)=-(-25x^2+164) \\ \Leftrightarrow 20x^2+16=25x^2-164 \\ \Leftrightarrow 20x^2-25x^2=-164-16 \\ \Leftrightarrow -5x^2 = -180 \\ \Leftrightarrow x^2 = \frac{-180}{-5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
7. \(3(-10x^2-8)=-(28x^2+26) \\ \Leftrightarrow -30x^2-24=-28x^2-26 \\ \Leftrightarrow -30x^2+28x^2=-26+24 \\ \Leftrightarrow -2x^2 = -2 \\ \Leftrightarrow x^2 = \frac{-2}{-2}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
8. \(x^2+153=3x^2-9 \\ \Leftrightarrow x^2-3x^2=-9-153 \\ \Leftrightarrow -2x^2 = -162 \\ \Leftrightarrow x^2 = \frac{-162}{-2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
9. \(-7x^2+120=-5x^2-8 \\ \Leftrightarrow -7x^2+5x^2=-8-120 \\ \Leftrightarrow -2x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
10. \(-x^2+31=-4x^2+4 \\ \Leftrightarrow -x^2+4x^2=4-31 \\ \Leftrightarrow 3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{3} < 0 \\ V = \varnothing \\ -----------------\)
11. \(2x^2-18=0 \\ \Leftrightarrow 2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{2}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
12. \(7x^2+28=0 \\ \Leftrightarrow 7x^2 = -28 \\ \Leftrightarrow x^2 = \frac{-28}{7} < 0 \\ V = \varnothing \\ -----------------\)