Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4(5x^2-9)=-(28x^2+92)\)
2. \(-4x^2+0=0\)
3. \(2(-6x^2+3)=-(15x^2+186)\)
4. \(-x^2-4=0\)
5. \(-3(7x^2-4)=-(27x^2-36)\)
6. \(3(3x^2-9)=-(-15x^2-123)\)
7. \(5x^2+70=8x^2-5\)
8. \(-5x^2+980=0\)
9. \(-x^2-3=4x^2+2\)
10. \(4x^2-1560=-4x^2+8\)
11. \(3x^2+432=0\)
12. \(2x^2-252=4x^2-10\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4(5x^2-9)=-(28x^2+92) \\ \Leftrightarrow -20x^2+36=-28x^2-92 \\ \Leftrightarrow -20x^2+28x^2=-92-36 \\ \Leftrightarrow 8x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{8} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-4x^2+0=0 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(2(-6x^2+3)=-(15x^2+186) \\ \Leftrightarrow -12x^2+6=-15x^2-186 \\ \Leftrightarrow -12x^2+15x^2=-186-6 \\ \Leftrightarrow 3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-x^2-4=0 \\ \Leftrightarrow -x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{-1} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-3(7x^2-4)=-(27x^2-36) \\ \Leftrightarrow -21x^2+12=-27x^2+36 \\ \Leftrightarrow -21x^2+27x^2=36-12 \\ \Leftrightarrow 6x^2 = 24 \\ \Leftrightarrow x^2 = \frac{24}{6}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
6. \(3(3x^2-9)=-(-15x^2-123) \\ \Leftrightarrow 9x^2-27=15x^2+123 \\ \Leftrightarrow 9x^2-15x^2=123+27 \\ \Leftrightarrow -6x^2 = 150 \\ \Leftrightarrow x^2 = \frac{150}{-6} < 0 \\ V = \varnothing \\ -----------------\)
7. \(5x^2+70=8x^2-5 \\ \Leftrightarrow 5x^2-8x^2=-5-70 \\ \Leftrightarrow -3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{-3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
8. \(-5x^2+980=0 \\ \Leftrightarrow -5x^2 = -980 \\ \Leftrightarrow x^2 = \frac{-980}{-5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
9. \(-x^2-3=4x^2+2 \\ \Leftrightarrow -x^2-4x^2=2+3 \\ \Leftrightarrow -5x^2 = 5 \\ \Leftrightarrow x^2 = \frac{5}{-5} < 0 \\ V = \varnothing \\ -----------------\)
10. \(4x^2-1560=-4x^2+8 \\ \Leftrightarrow 4x^2+4x^2=8+1560 \\ \Leftrightarrow 8x^2 = 1568 \\ \Leftrightarrow x^2 = \frac{1568}{8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
11. \(3x^2+432=0 \\ \Leftrightarrow 3x^2 = -432 \\ \Leftrightarrow x^2 = \frac{-432}{3} < 0 \\ V = \varnothing \\ -----------------\)
12. \(2x^2-252=4x^2-10 \\ \Leftrightarrow 2x^2-4x^2=-10+252 \\ \Leftrightarrow -2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{-2} < 0 \\ V = \varnothing \\ -----------------\)