Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3x^2+6=8x^2+6\)
2. \(-3(8x^2+8)=-(21x^2-84)\)
3. \(-5(5x^2-9)=-(27x^2-437)\)
4. \(8x^2+0=0\)
5. \(-5x^2-605=0\)
6. \(5(-2x^2-6)=-(16x^2-186)\)
7. \(6x^2+24=0\)
8. \(11x^2-595=6x^2+10\)
9. \(11x^2-849=4x^2-2\)
10. \(-3(-9x^2-10)=-(-24x^2+45)\)
11. \(-10x^2-656=-2x^2-8\)
12. \(-4x^2+400=-9x^2-5\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3x^2+6=8x^2+6 \\ \Leftrightarrow 3x^2-8x^2=6-6 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-3(8x^2+8)=-(21x^2-84) \\ \Leftrightarrow -24x^2-24=-21x^2+84 \\ \Leftrightarrow -24x^2+21x^2=84+24 \\ \Leftrightarrow -3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{-3} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-5(5x^2-9)=-(27x^2-437) \\ \Leftrightarrow -25x^2+45=-27x^2+437 \\ \Leftrightarrow -25x^2+27x^2=437-45 \\ \Leftrightarrow 2x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{2}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
4. \(8x^2+0=0 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(-5x^2-605=0 \\ \Leftrightarrow -5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{-5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(5(-2x^2-6)=-(16x^2-186) \\ \Leftrightarrow -10x^2-30=-16x^2+186 \\ \Leftrightarrow -10x^2+16x^2=186+30 \\ \Leftrightarrow 6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{6}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
7. \(6x^2+24=0 \\ \Leftrightarrow 6x^2 = -24 \\ \Leftrightarrow x^2 = \frac{-24}{6} < 0 \\ V = \varnothing \\ -----------------\)
8. \(11x^2-595=6x^2+10 \\ \Leftrightarrow 11x^2-6x^2=10+595 \\ \Leftrightarrow 5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(11x^2-849=4x^2-2 \\ \Leftrightarrow 11x^2-4x^2=-2+849 \\ \Leftrightarrow 7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
10. \(-3(-9x^2-10)=-(-24x^2+45) \\ \Leftrightarrow 27x^2+30=24x^2-45 \\ \Leftrightarrow 27x^2-24x^2=-45-30 \\ \Leftrightarrow 3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{3} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-10x^2-656=-2x^2-8 \\ \Leftrightarrow -10x^2+2x^2=-8+656 \\ \Leftrightarrow -8x^2 = 648 \\ \Leftrightarrow x^2 = \frac{648}{-8} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-4x^2+400=-9x^2-5 \\ \Leftrightarrow -4x^2+9x^2=-5-400 \\ \Leftrightarrow 5x^2 = -405 \\ \Leftrightarrow x^2 = \frac{-405}{5} < 0 \\ V = \varnothing \\ -----------------\)