Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(9x^2+610=4x^2+5\)
2. \(-11x^2+259=-7x^2+3\)
3. \(5(2x^2+5)=-(-17x^2+150)\)
4. \(-11x^2+74=-10x^2+10\)
5. \(5x^2-20=0\)
6. \(7x^2-252=0\)
7. \(-4x^2+836=-9x^2-9\)
8. \(-5(10x^2-8)=-(45x^2+565)\)
9. \(14x^2-10=8x^2-4\)
10. \(2x^2-128=0\)
11. \(-5(-6x^2-5)=-(-25x^2-25)\)
12. \(2x^2-5=7x^2-10\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(9x^2+610=4x^2+5 \\ \Leftrightarrow 9x^2-4x^2=5-610 \\ \Leftrightarrow 5x^2 = -605 \\ \Leftrightarrow x^2 = \frac{-605}{5} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-11x^2+259=-7x^2+3 \\ \Leftrightarrow -11x^2+7x^2=3-259 \\ \Leftrightarrow -4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{-4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
3. \(5(2x^2+5)=-(-17x^2+150) \\ \Leftrightarrow 10x^2+25=17x^2-150 \\ \Leftrightarrow 10x^2-17x^2=-150-25 \\ \Leftrightarrow -7x^2 = -175 \\ \Leftrightarrow x^2 = \frac{-175}{-7}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
4. \(-11x^2+74=-10x^2+10 \\ \Leftrightarrow -11x^2+10x^2=10-74 \\ \Leftrightarrow -x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-1}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(5x^2-20=0 \\ \Leftrightarrow 5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
6. \(7x^2-252=0 \\ \Leftrightarrow 7x^2 = 252 \\ \Leftrightarrow x^2 = \frac{252}{7}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
7. \(-4x^2+836=-9x^2-9 \\ \Leftrightarrow -4x^2+9x^2=-9-836 \\ \Leftrightarrow 5x^2 = -845 \\ \Leftrightarrow x^2 = \frac{-845}{5} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-5(10x^2-8)=-(45x^2+565) \\ \Leftrightarrow -50x^2+40=-45x^2-565 \\ \Leftrightarrow -50x^2+45x^2=-565-40 \\ \Leftrightarrow -5x^2 = -605 \\ \Leftrightarrow x^2 = \frac{-605}{-5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(14x^2-10=8x^2-4 \\ \Leftrightarrow 14x^2-8x^2=-4+10 \\ \Leftrightarrow 6x^2 = 6 \\ \Leftrightarrow x^2 = \frac{6}{6}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
10. \(2x^2-128=0 \\ \Leftrightarrow 2x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
11. \(-5(-6x^2-5)=-(-25x^2-25) \\ \Leftrightarrow 30x^2+25=25x^2+25 \\ \Leftrightarrow 30x^2-25x^2=25-25 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(2x^2-5=7x^2-10 \\ \Leftrightarrow 2x^2-7x^2=-10+5 \\ \Leftrightarrow -5x^2 = -5 \\ \Leftrightarrow x^2 = \frac{-5}{-5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)