Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4(-3x^2-5)=-(-14x^2-182)\)
2. \(5x^2+4=-2x^2+4\)
3. \(x^2-96=-3x^2+4\)
4. \(2(-5x^2-5)=-(8x^2-278)\)
5. \(3x^2-125=2x^2-4\)
6. \(-8x^2+200=0\)
7. \(-14x^2+908=-10x^2+8\)
8. \(8x^2-32=0\)
9. \(-5(-2x^2-9)=-(-17x^2-45)\)
10. \(-5(10x^2-9)=-(44x^2-339)\)
11. \(8x^2+8=0\)
12. \(-x^2+26=4x^2+6\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4(-3x^2-5)=-(-14x^2-182) \\ \Leftrightarrow 12x^2+20=14x^2+182 \\ \Leftrightarrow 12x^2-14x^2=182-20 \\ \Leftrightarrow -2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{-2} < 0 \\ V = \varnothing \\ -----------------\)
2. \(5x^2+4=-2x^2+4 \\ \Leftrightarrow 5x^2+2x^2=4-4 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(x^2-96=-3x^2+4 \\ \Leftrightarrow x^2+3x^2=4+96 \\ \Leftrightarrow 4x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{4}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
4. \(2(-5x^2-5)=-(8x^2-278) \\ \Leftrightarrow -10x^2-10=-8x^2+278 \\ \Leftrightarrow -10x^2+8x^2=278+10 \\ \Leftrightarrow -2x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{-2} < 0 \\ V = \varnothing \\ -----------------\)
5. \(3x^2-125=2x^2-4 \\ \Leftrightarrow 3x^2-2x^2=-4+125 \\ \Leftrightarrow x^2 = 121 \\ \Leftrightarrow x^2 = \frac{121}{1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
6. \(-8x^2+200=0 \\ \Leftrightarrow -8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
7. \(-14x^2+908=-10x^2+8 \\ \Leftrightarrow -14x^2+10x^2=8-908 \\ \Leftrightarrow -4x^2 = -900 \\ \Leftrightarrow x^2 = \frac{-900}{-4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
8. \(8x^2-32=0 \\ \Leftrightarrow 8x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
9. \(-5(-2x^2-9)=-(-17x^2-45) \\ \Leftrightarrow 10x^2+45=17x^2+45 \\ \Leftrightarrow 10x^2-17x^2=45-45 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(-5(10x^2-9)=-(44x^2-339) \\ \Leftrightarrow -50x^2+45=-44x^2+339 \\ \Leftrightarrow -50x^2+44x^2=339-45 \\ \Leftrightarrow -6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{-6} < 0 \\ V = \varnothing \\ -----------------\)
11. \(8x^2+8=0 \\ \Leftrightarrow 8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{8} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-x^2+26=4x^2+6 \\ \Leftrightarrow -x^2-4x^2=6-26 \\ \Leftrightarrow -5x^2 = -20 \\ \Leftrightarrow x^2 = \frac{-20}{-5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)