Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(4x^2-5)=-(14x^2-121)\)
2. \(x^2+978=6x^2-2\)
3. \(-5(-5x^2+9)=-(-26x^2+109)\)
4. \(-7x^2-343=0\)
5. \(-3(-3x^2+3)=-(-5x^2-391)\)
6. \(2(-2x^2-7)=-(10x^2-1162)\)
7. \(17x^2-845=10x^2+2\)
8. \(-11x^2+1123=-6x^2-2\)
9. \(-3(7x^2+9)=-(23x^2+77)\)
10. \(6x^2-136=-2x^2-8\)
11. \(-4(-7x^2+3)=-(-22x^2-282)\)
12. \(10x^2-117=9x^2+4\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(4x^2-5)=-(14x^2-121) \\ \Leftrightarrow -20x^2+25=-14x^2+121 \\ \Leftrightarrow -20x^2+14x^2=121-25 \\ \Leftrightarrow -6x^2 = 96 \\ \Leftrightarrow x^2 = \frac{96}{-6} < 0 \\ V = \varnothing \\ -----------------\)
2. \(x^2+978=6x^2-2 \\ \Leftrightarrow x^2-6x^2=-2-978 \\ \Leftrightarrow -5x^2 = -980 \\ \Leftrightarrow x^2 = \frac{-980}{-5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
3. \(-5(-5x^2+9)=-(-26x^2+109) \\ \Leftrightarrow 25x^2-45=26x^2-109 \\ \Leftrightarrow 25x^2-26x^2=-109+45 \\ \Leftrightarrow -x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-1}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
4. \(-7x^2-343=0 \\ \Leftrightarrow -7x^2 = 343 \\ \Leftrightarrow x^2 = \frac{343}{-7} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-3(-3x^2+3)=-(-5x^2-391) \\ \Leftrightarrow 9x^2-9=5x^2+391 \\ \Leftrightarrow 9x^2-5x^2=391+9 \\ \Leftrightarrow 4x^2 = 400 \\ \Leftrightarrow x^2 = \frac{400}{4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
6. \(2(-2x^2-7)=-(10x^2-1162) \\ \Leftrightarrow -4x^2-14=-10x^2+1162 \\ \Leftrightarrow -4x^2+10x^2=1162+14 \\ \Leftrightarrow 6x^2 = 1176 \\ \Leftrightarrow x^2 = \frac{1176}{6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
7. \(17x^2-845=10x^2+2 \\ \Leftrightarrow 17x^2-10x^2=2+845 \\ \Leftrightarrow 7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
8. \(-11x^2+1123=-6x^2-2 \\ \Leftrightarrow -11x^2+6x^2=-2-1123 \\ \Leftrightarrow -5x^2 = -1125 \\ \Leftrightarrow x^2 = \frac{-1125}{-5}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
9. \(-3(7x^2+9)=-(23x^2+77) \\ \Leftrightarrow -21x^2-27=-23x^2-77 \\ \Leftrightarrow -21x^2+23x^2=-77+27 \\ \Leftrightarrow 2x^2 = -50 \\ \Leftrightarrow x^2 = \frac{-50}{2} < 0 \\ V = \varnothing \\ -----------------\)
10. \(6x^2-136=-2x^2-8 \\ \Leftrightarrow 6x^2+2x^2=-8+136 \\ \Leftrightarrow 8x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{8}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(-4(-7x^2+3)=-(-22x^2-282) \\ \Leftrightarrow 28x^2-12=22x^2+282 \\ \Leftrightarrow 28x^2-22x^2=282+12 \\ \Leftrightarrow 6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
12. \(10x^2-117=9x^2+4 \\ \Leftrightarrow 10x^2-9x^2=4+117 \\ \Leftrightarrow x^2 = 121 \\ \Leftrightarrow x^2 = \frac{121}{1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)