Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2+290=9x^2+2\)
2. \(-12x^2-173=-5x^2+2\)
3. \(7x^2-7=0\)
4. \(9x^2+443=7x^2-7\)
5. \(x^2-441=-2x^2-9\)
6. \(4(-2x^2+2)=-(0x^2+0)\)
7. \(4(-10x^2-4)=-(37x^2+259)\)
8. \(-5(3x^2-5)=-(13x^2+73)\)
9. \(-3x^2-300=0\)
10. \(-11x^2-4=-6x^2-4\)
11. \(-2(4x^2-9)=-(6x^2+32)\)
12. \(6x^2+0=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2+290=9x^2+2 \\ \Leftrightarrow x^2-9x^2=2-290 \\ \Leftrightarrow -8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
2. \(-12x^2-173=-5x^2+2 \\ \Leftrightarrow -12x^2+5x^2=2+173 \\ \Leftrightarrow -7x^2 = 175 \\ \Leftrightarrow x^2 = \frac{175}{-7} < 0 \\ V = \varnothing \\ -----------------\)
3. \(7x^2-7=0 \\ \Leftrightarrow 7x^2 = 7 \\ \Leftrightarrow x^2 = \frac{7}{7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
4. \(9x^2+443=7x^2-7 \\ \Leftrightarrow 9x^2-7x^2=-7-443 \\ \Leftrightarrow 2x^2 = -450 \\ \Leftrightarrow x^2 = \frac{-450}{2} < 0 \\ V = \varnothing \\ -----------------\)
5. \(x^2-441=-2x^2-9 \\ \Leftrightarrow x^2+2x^2=-9+441 \\ \Leftrightarrow 3x^2 = 432 \\ \Leftrightarrow x^2 = \frac{432}{3}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
6. \(4(-2x^2+2)=-(0x^2+0) \\ \Leftrightarrow -8x^2+8=0x^2+0 \\ \Leftrightarrow -8x^2+0x^2=0-8 \\ \Leftrightarrow -8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
7. \(4(-10x^2-4)=-(37x^2+259) \\ \Leftrightarrow -40x^2-16=-37x^2-259 \\ \Leftrightarrow -40x^2+37x^2=-259+16 \\ \Leftrightarrow -3x^2 = -243 \\ \Leftrightarrow x^2 = \frac{-243}{-3}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
8. \(-5(3x^2-5)=-(13x^2+73) \\ \Leftrightarrow -15x^2+25=-13x^2-73 \\ \Leftrightarrow -15x^2+13x^2=-73-25 \\ \Leftrightarrow -2x^2 = -98 \\ \Leftrightarrow x^2 = \frac{-98}{-2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
9. \(-3x^2-300=0 \\ \Leftrightarrow -3x^2 = 300 \\ \Leftrightarrow x^2 = \frac{300}{-3} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-11x^2-4=-6x^2-4 \\ \Leftrightarrow -11x^2+6x^2=-4+4 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-2(4x^2-9)=-(6x^2+32) \\ \Leftrightarrow -8x^2+18=-6x^2-32 \\ \Leftrightarrow -8x^2+6x^2=-32-18 \\ \Leftrightarrow -2x^2 = -50 \\ \Leftrightarrow x^2 = \frac{-50}{-2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
12. \(6x^2+0=0 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)