Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2-100=0\)
2. \(11x^2-8=8x^2-5\)
3. \(3x^2-7=6x^2-10\)
4. \(-3(-6x^2-6)=-(-14x^2-274)\)
5. \(5(6x^2-10)=-(-23x^2-293)\)
6. \(5x^2-980=0\)
7. \(-4(3x^2-2)=-(14x^2+10)\)
8. \(-2x^2-521=-10x^2-9\)
9. \(-5x^2-180=0\)
10. \(x^2+34=9x^2+2\)
11. \(4(7x^2-6)=-(-20x^2+24)\)
12. \(4x^2-144=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2-100=0 \\ \Leftrightarrow -4x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{-4} < 0 \\ V = \varnothing \\ -----------------\)
2. \(11x^2-8=8x^2-5 \\ \Leftrightarrow 11x^2-8x^2=-5+8 \\ \Leftrightarrow 3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
3. \(3x^2-7=6x^2-10 \\ \Leftrightarrow 3x^2-6x^2=-10+7 \\ \Leftrightarrow -3x^2 = -3 \\ \Leftrightarrow x^2 = \frac{-3}{-3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
4. \(-3(-6x^2-6)=-(-14x^2-274) \\ \Leftrightarrow 18x^2+18=14x^2+274 \\ \Leftrightarrow 18x^2-14x^2=274-18 \\ \Leftrightarrow 4x^2 = 256 \\ \Leftrightarrow x^2 = \frac{256}{4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(5(6x^2-10)=-(-23x^2-293) \\ \Leftrightarrow 30x^2-50=23x^2+293 \\ \Leftrightarrow 30x^2-23x^2=293+50 \\ \Leftrightarrow 7x^2 = 343 \\ \Leftrightarrow x^2 = \frac{343}{7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
6. \(5x^2-980=0 \\ \Leftrightarrow 5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
7. \(-4(3x^2-2)=-(14x^2+10) \\ \Leftrightarrow -12x^2+8=-14x^2-10 \\ \Leftrightarrow -12x^2+14x^2=-10-8 \\ \Leftrightarrow 2x^2 = -18 \\ \Leftrightarrow x^2 = \frac{-18}{2} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-2x^2-521=-10x^2-9 \\ \Leftrightarrow -2x^2+10x^2=-9+521 \\ \Leftrightarrow 8x^2 = 512 \\ \Leftrightarrow x^2 = \frac{512}{8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
9. \(-5x^2-180=0 \\ \Leftrightarrow -5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{-5} < 0 \\ V = \varnothing \\ -----------------\)
10. \(x^2+34=9x^2+2 \\ \Leftrightarrow x^2-9x^2=2-34 \\ \Leftrightarrow -8x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{-8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
11. \(4(7x^2-6)=-(-20x^2+24) \\ \Leftrightarrow 28x^2-24=20x^2-24 \\ \Leftrightarrow 28x^2-20x^2=-24+24 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(4x^2-144=0 \\ \Leftrightarrow 4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)