Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(-5x^2-10)=-(26x^2+54)\)
2. \(-10x^2-894=-6x^2+6\)
3. \(-4x^2-190=-7x^2+2\)
4. \(-4(-9x^2+4)=-(-34x^2-34)\)
5. \(x^2-159=2x^2+10\)
6. \(5(-5x^2+6)=-(31x^2-180)\)
7. \(14x^2-392=10x^2+8\)
8. \(4(9x^2-6)=-(-28x^2+312)\)
9. \(15x^2+518=7x^2+6\)
10. \(-7x^2+184=-4x^2-8\)
11. \(-5(-6x^2-2)=-(-29x^2-1)\)
12. \(-2(5x^2+5)=-(9x^2+10)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(-5x^2-10)=-(26x^2+54) \\ \Leftrightarrow -25x^2-50=-26x^2-54 \\ \Leftrightarrow -25x^2+26x^2=-54+50 \\ \Leftrightarrow x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-10x^2-894=-6x^2+6 \\ \Leftrightarrow -10x^2+6x^2=6+894 \\ \Leftrightarrow -4x^2 = 900 \\ \Leftrightarrow x^2 = \frac{900}{-4} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-4x^2-190=-7x^2+2 \\ \Leftrightarrow -4x^2+7x^2=2+190 \\ \Leftrightarrow 3x^2 = 192 \\ \Leftrightarrow x^2 = \frac{192}{3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
4. \(-4(-9x^2+4)=-(-34x^2-34) \\ \Leftrightarrow 36x^2-16=34x^2+34 \\ \Leftrightarrow 36x^2-34x^2=34+16 \\ \Leftrightarrow 2x^2 = 50 \\ \Leftrightarrow x^2 = \frac{50}{2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(x^2-159=2x^2+10 \\ \Leftrightarrow x^2-2x^2=10+159 \\ \Leftrightarrow -x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{-1} < 0 \\ V = \varnothing \\ -----------------\)
6. \(5(-5x^2+6)=-(31x^2-180) \\ \Leftrightarrow -25x^2+30=-31x^2+180 \\ \Leftrightarrow -25x^2+31x^2=180-30 \\ \Leftrightarrow 6x^2 = 150 \\ \Leftrightarrow x^2 = \frac{150}{6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
7. \(14x^2-392=10x^2+8 \\ \Leftrightarrow 14x^2-10x^2=8+392 \\ \Leftrightarrow 4x^2 = 400 \\ \Leftrightarrow x^2 = \frac{400}{4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
8. \(4(9x^2-6)=-(-28x^2+312) \\ \Leftrightarrow 36x^2-24=28x^2-312 \\ \Leftrightarrow 36x^2-28x^2=-312+24 \\ \Leftrightarrow 8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{8} < 0 \\ V = \varnothing \\ -----------------\)
9. \(15x^2+518=7x^2+6 \\ \Leftrightarrow 15x^2-7x^2=6-518 \\ \Leftrightarrow 8x^2 = -512 \\ \Leftrightarrow x^2 = \frac{-512}{8} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-7x^2+184=-4x^2-8 \\ \Leftrightarrow -7x^2+4x^2=-8-184 \\ \Leftrightarrow -3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{-3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
11. \(-5(-6x^2-2)=-(-29x^2-1) \\ \Leftrightarrow 30x^2+10=29x^2+1 \\ \Leftrightarrow 30x^2-29x^2=1-10 \\ \Leftrightarrow x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{1} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-2(5x^2+5)=-(9x^2+10) \\ \Leftrightarrow -10x^2-10=-9x^2-10 \\ \Leftrightarrow -10x^2+9x^2=-10+10 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)