Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2-1350=0\)
2. \(14x^2+507=9x^2+7\)
3. \(x^2-1374=8x^2-2\)
4. \(12x^2-45=10x^2+5\)
5. \(-2x^2-162=0\)
6. \(-2(-2x^2-6)=-(2x^2-306)\)
7. \(-2x^2+8=-4x^2+10\)
8. \(-9x^2+238=-7x^2-4\)
9. \(5x^2+2=6x^2-7\)
10. \(4x^2+2=5x^2+2\)
11. \(3(5x^2+2)=-(-8x^2-573)\)
12. \(7x^2+24=9x^2+6\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2-1350=0 \\ \Leftrightarrow -6x^2 = 1350 \\ \Leftrightarrow x^2 = \frac{1350}{-6} < 0 \\ V = \varnothing \\ -----------------\)
2. \(14x^2+507=9x^2+7 \\ \Leftrightarrow 14x^2-9x^2=7-507 \\ \Leftrightarrow 5x^2 = -500 \\ \Leftrightarrow x^2 = \frac{-500}{5} < 0 \\ V = \varnothing \\ -----------------\)
3. \(x^2-1374=8x^2-2 \\ \Leftrightarrow x^2-8x^2=-2+1374 \\ \Leftrightarrow -7x^2 = 1372 \\ \Leftrightarrow x^2 = \frac{1372}{-7} < 0 \\ V = \varnothing \\ -----------------\)
4. \(12x^2-45=10x^2+5 \\ \Leftrightarrow 12x^2-10x^2=5+45 \\ \Leftrightarrow 2x^2 = 50 \\ \Leftrightarrow x^2 = \frac{50}{2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(-2x^2-162=0 \\ \Leftrightarrow -2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{-2} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-2(-2x^2-6)=-(2x^2-306) \\ \Leftrightarrow 4x^2+12=-2x^2+306 \\ \Leftrightarrow 4x^2+2x^2=306-12 \\ \Leftrightarrow 6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
7. \(-2x^2+8=-4x^2+10 \\ \Leftrightarrow -2x^2+4x^2=10-8 \\ \Leftrightarrow 2x^2 = 2 \\ \Leftrightarrow x^2 = \frac{2}{2}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
8. \(-9x^2+238=-7x^2-4 \\ \Leftrightarrow -9x^2+7x^2=-4-238 \\ \Leftrightarrow -2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{-2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(5x^2+2=6x^2-7 \\ \Leftrightarrow 5x^2-6x^2=-7-2 \\ \Leftrightarrow -x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{-1}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
10. \(4x^2+2=5x^2+2 \\ \Leftrightarrow 4x^2-5x^2=2-2 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(3(5x^2+2)=-(-8x^2-573) \\ \Leftrightarrow 15x^2+6=8x^2+573 \\ \Leftrightarrow 15x^2-8x^2=573-6 \\ \Leftrightarrow 7x^2 = 567 \\ \Leftrightarrow x^2 = \frac{567}{7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
12. \(7x^2+24=9x^2+6 \\ \Leftrightarrow 7x^2-9x^2=6-24 \\ \Leftrightarrow -2x^2 = -18 \\ \Leftrightarrow x^2 = \frac{-18}{-2}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)