Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(10x^2-3)=-(57x^2-1590)\)
2. \(-2(-2x^2-7)=-(-3x^2+182)\)
3. \(2x^2+72=0\)
4. \(6x^2-294=0\)
5. \(x^2+59=7x^2+5\)
6. \(11x^2-319=7x^2+5\)
7. \(-3(2x^2-5)=-(5x^2-15)\)
8. \(5(9x^2-8)=-(-37x^2-472)\)
9. \(4x^2+355=7x^2-8\)
10. \(3(-3x^2+10)=-(13x^2-174)\)
11. \(2x^2+29=3x^2-7\)
12. \(5(6x^2+9)=-(-35x^2+200)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(10x^2-3)=-(57x^2-1590) \\ \Leftrightarrow -50x^2+15=-57x^2+1590 \\ \Leftrightarrow -50x^2+57x^2=1590-15 \\ \Leftrightarrow 7x^2 = 1575 \\ \Leftrightarrow x^2 = \frac{1575}{7}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
2. \(-2(-2x^2-7)=-(-3x^2+182) \\ \Leftrightarrow 4x^2+14=3x^2-182 \\ \Leftrightarrow 4x^2-3x^2=-182-14 \\ \Leftrightarrow x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{1} < 0 \\ V = \varnothing \\ -----------------\)
3. \(2x^2+72=0 \\ \Leftrightarrow 2x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{2} < 0 \\ V = \varnothing \\ -----------------\)
4. \(6x^2-294=0 \\ \Leftrightarrow 6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
5. \(x^2+59=7x^2+5 \\ \Leftrightarrow x^2-7x^2=5-59 \\ \Leftrightarrow -6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{-6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
6. \(11x^2-319=7x^2+5 \\ \Leftrightarrow 11x^2-7x^2=5+319 \\ \Leftrightarrow 4x^2 = 324 \\ \Leftrightarrow x^2 = \frac{324}{4}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
7. \(-3(2x^2-5)=-(5x^2-15) \\ \Leftrightarrow -6x^2+15=-5x^2+15 \\ \Leftrightarrow -6x^2+5x^2=15-15 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(5(9x^2-8)=-(-37x^2-472) \\ \Leftrightarrow 45x^2-40=37x^2+472 \\ \Leftrightarrow 45x^2-37x^2=472+40 \\ \Leftrightarrow 8x^2 = 512 \\ \Leftrightarrow x^2 = \frac{512}{8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
9. \(4x^2+355=7x^2-8 \\ \Leftrightarrow 4x^2-7x^2=-8-355 \\ \Leftrightarrow -3x^2 = -363 \\ \Leftrightarrow x^2 = \frac{-363}{-3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
10. \(3(-3x^2+10)=-(13x^2-174) \\ \Leftrightarrow -9x^2+30=-13x^2+174 \\ \Leftrightarrow -9x^2+13x^2=174-30 \\ \Leftrightarrow 4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
11. \(2x^2+29=3x^2-7 \\ \Leftrightarrow 2x^2-3x^2=-7-29 \\ \Leftrightarrow -x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-1}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
12. \(5(6x^2+9)=-(-35x^2+200) \\ \Leftrightarrow 30x^2+45=35x^2-200 \\ \Leftrightarrow 30x^2-35x^2=-200-45 \\ \Leftrightarrow -5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{-5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)