Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(-3x^2+10)=-(-17x^2-22)\)
2. \(6x^2-384=0\)
3. \(-4(-6x^2+5)=-(-23x^2+20)\)
4. \(-13x^2+7=-8x^2+7\)
5. \(-3(5x^2-6)=-(8x^2+1557)\)
6. \(4(-10x^2-3)=-(34x^2+108)\)
7. \(3x^2+300=0\)
8. \(-4(9x^2+3)=-(28x^2+12)\)
9. \(-3x^2-588=0\)
10. \(7x^2-219=8x^2+6\)
11. \(-6x^2-6=0\)
12. \(-6x^2-14=-8x^2-6\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(-3x^2+10)=-(-17x^2-22) \\ \Leftrightarrow 15x^2-50=17x^2+22 \\ \Leftrightarrow 15x^2-17x^2=22+50 \\ \Leftrightarrow -2x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{-2} < 0 \\ V = \varnothing \\ -----------------\)
2. \(6x^2-384=0 \\ \Leftrightarrow 6x^2 = 384 \\ \Leftrightarrow x^2 = \frac{384}{6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
3. \(-4(-6x^2+5)=-(-23x^2+20) \\ \Leftrightarrow 24x^2-20=23x^2-20 \\ \Leftrightarrow 24x^2-23x^2=-20+20 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-13x^2+7=-8x^2+7 \\ \Leftrightarrow -13x^2+8x^2=7-7 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(-3(5x^2-6)=-(8x^2+1557) \\ \Leftrightarrow -15x^2+18=-8x^2-1557 \\ \Leftrightarrow -15x^2+8x^2=-1557-18 \\ \Leftrightarrow -7x^2 = -1575 \\ \Leftrightarrow x^2 = \frac{-1575}{-7}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
6. \(4(-10x^2-3)=-(34x^2+108) \\ \Leftrightarrow -40x^2-12=-34x^2-108 \\ \Leftrightarrow -40x^2+34x^2=-108+12 \\ \Leftrightarrow -6x^2 = -96 \\ \Leftrightarrow x^2 = \frac{-96}{-6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
7. \(3x^2+300=0 \\ \Leftrightarrow 3x^2 = -300 \\ \Leftrightarrow x^2 = \frac{-300}{3} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-4(9x^2+3)=-(28x^2+12) \\ \Leftrightarrow -36x^2-12=-28x^2-12 \\ \Leftrightarrow -36x^2+28x^2=-12+12 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(-3x^2-588=0 \\ \Leftrightarrow -3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{-3} < 0 \\ V = \varnothing \\ -----------------\)
10. \(7x^2-219=8x^2+6 \\ \Leftrightarrow 7x^2-8x^2=6+219 \\ \Leftrightarrow -x^2 = 225 \\ \Leftrightarrow x^2 = \frac{225}{-1} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-6x^2-6=0 \\ \Leftrightarrow -6x^2 = 6 \\ \Leftrightarrow x^2 = \frac{6}{-6} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-6x^2-14=-8x^2-6 \\ \Leftrightarrow -6x^2+8x^2=-6+14 \\ \Leftrightarrow 2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)