Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5x^2-980=0\)
2. \(-4(9x^2-6)=-(32x^2+40)\)
3. \(-3(-9x^2+5)=-(-19x^2+143)\)
4. \(-5(-8x^2+8)=-(-43x^2+40)\)
5. \(8x^2+0=0\)
6. \(6x^2-10=4x^2+8\)
7. \(-12x^2-188=-7x^2-8\)
8. \(-9x^2+376=-3x^2-8\)
9. \(4(7x^2-10)=-(-30x^2+168)\)
10. \(3x^2-363=0\)
11. \(-6x^2+172=-4x^2+10\)
12. \(-5(4x^2+7)=-(25x^2+15)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5x^2-980=0 \\ \Leftrightarrow -5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{-5} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-4(9x^2-6)=-(32x^2+40) \\ \Leftrightarrow -36x^2+24=-32x^2-40 \\ \Leftrightarrow -36x^2+32x^2=-40-24 \\ \Leftrightarrow -4x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
3. \(-3(-9x^2+5)=-(-19x^2+143) \\ \Leftrightarrow 27x^2-15=19x^2-143 \\ \Leftrightarrow 27x^2-19x^2=-143+15 \\ \Leftrightarrow 8x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{8} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-5(-8x^2+8)=-(-43x^2+40) \\ \Leftrightarrow 40x^2-40=43x^2-40 \\ \Leftrightarrow 40x^2-43x^2=-40+40 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(8x^2+0=0 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(6x^2-10=4x^2+8 \\ \Leftrightarrow 6x^2-4x^2=8+10 \\ \Leftrightarrow 2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{2}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
7. \(-12x^2-188=-7x^2-8 \\ \Leftrightarrow -12x^2+7x^2=-8+188 \\ \Leftrightarrow -5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{-5} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-9x^2+376=-3x^2-8 \\ \Leftrightarrow -9x^2+3x^2=-8-376 \\ \Leftrightarrow -6x^2 = -384 \\ \Leftrightarrow x^2 = \frac{-384}{-6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
9. \(4(7x^2-10)=-(-30x^2+168) \\ \Leftrightarrow 28x^2-40=30x^2-168 \\ \Leftrightarrow 28x^2-30x^2=-168+40 \\ \Leftrightarrow -2x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
10. \(3x^2-363=0 \\ \Leftrightarrow 3x^2 = 363 \\ \Leftrightarrow x^2 = \frac{363}{3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
11. \(-6x^2+172=-4x^2+10 \\ \Leftrightarrow -6x^2+4x^2=10-172 \\ \Leftrightarrow -2x^2 = -162 \\ \Leftrightarrow x^2 = \frac{-162}{-2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
12. \(-5(4x^2+7)=-(25x^2+15) \\ \Leftrightarrow -20x^2-35=-25x^2-15 \\ \Leftrightarrow -20x^2+25x^2=-15+35 \\ \Leftrightarrow 5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)