Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2-49=0\)
2. \(8x^2+1152=0\)
3. \(15x^2-1567=8x^2+8\)
4. \(4(-8x^2-7)=-(34x^2+30)\)
5. \(-17x^2-2=-10x^2-9\)
6. \(4(4x^2-9)=-(-11x^2+881)\)
7. \(-4(4x^2+4)=-(24x^2-952)\)
8. \(-3(-4x^2+2)=-(-9x^2+438)\)
9. \(2(8x^2+2)=-(-12x^2+12)\)
10. \(-4(9x^2+3)=-(29x^2+460)\)
11. \(4(-7x^2-10)=-(33x^2+40)\)
12. \(4x^2-400=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2-49=0 \\ \Leftrightarrow x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(8x^2+1152=0 \\ \Leftrightarrow 8x^2 = -1152 \\ \Leftrightarrow x^2 = \frac{-1152}{8} < 0 \\ V = \varnothing \\ -----------------\)
3. \(15x^2-1567=8x^2+8 \\ \Leftrightarrow 15x^2-8x^2=8+1567 \\ \Leftrightarrow 7x^2 = 1575 \\ \Leftrightarrow x^2 = \frac{1575}{7}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
4. \(4(-8x^2-7)=-(34x^2+30) \\ \Leftrightarrow -32x^2-28=-34x^2-30 \\ \Leftrightarrow -32x^2+34x^2=-30+28 \\ \Leftrightarrow 2x^2 = -2 \\ \Leftrightarrow x^2 = \frac{-2}{2} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-17x^2-2=-10x^2-9 \\ \Leftrightarrow -17x^2+10x^2=-9+2 \\ \Leftrightarrow -7x^2 = -7 \\ \Leftrightarrow x^2 = \frac{-7}{-7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(4(4x^2-9)=-(-11x^2+881) \\ \Leftrightarrow 16x^2-36=11x^2-881 \\ \Leftrightarrow 16x^2-11x^2=-881+36 \\ \Leftrightarrow 5x^2 = -845 \\ \Leftrightarrow x^2 = \frac{-845}{5} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-4(4x^2+4)=-(24x^2-952) \\ \Leftrightarrow -16x^2-16=-24x^2+952 \\ \Leftrightarrow -16x^2+24x^2=952+16 \\ \Leftrightarrow 8x^2 = 968 \\ \Leftrightarrow x^2 = \frac{968}{8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
8. \(-3(-4x^2+2)=-(-9x^2+438) \\ \Leftrightarrow 12x^2-6=9x^2-438 \\ \Leftrightarrow 12x^2-9x^2=-438+6 \\ \Leftrightarrow 3x^2 = -432 \\ \Leftrightarrow x^2 = \frac{-432}{3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(2(8x^2+2)=-(-12x^2+12) \\ \Leftrightarrow 16x^2+4=12x^2-12 \\ \Leftrightarrow 16x^2-12x^2=-12-4 \\ \Leftrightarrow 4x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{4} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-4(9x^2+3)=-(29x^2+460) \\ \Leftrightarrow -36x^2-12=-29x^2-460 \\ \Leftrightarrow -36x^2+29x^2=-460+12 \\ \Leftrightarrow -7x^2 = -448 \\ \Leftrightarrow x^2 = \frac{-448}{-7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
11. \(4(-7x^2-10)=-(33x^2+40) \\ \Leftrightarrow -28x^2-40=-33x^2-40 \\ \Leftrightarrow -28x^2+33x^2=-40+40 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(4x^2-400=0 \\ \Leftrightarrow 4x^2 = 400 \\ \Leftrightarrow x^2 = \frac{400}{4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)