Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2+718=2x^2-8\)
2. \(-8x^2+385=-6x^2-7\)
3. \(-4(-8x^2+7)=-(-31x^2+53)\)
4. \(-2(5x^2+10)=-(6x^2+344)\)
5. \(3(8x^2+2)=-(-17x^2-1189)\)
6. \(-5x^2+180=0\)
7. \(11x^2+6=10x^2-3\)
8. \(5x^2-180=0\)
9. \(6x^2+426=9x^2-6\)
10. \(3(-2x^2-10)=-(2x^2+26)\)
11. \(9x^2+3=7x^2+3\)
12. \(-4(-10x^2+8)=-(-39x^2-4)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2+718=2x^2-8 \\ \Leftrightarrow -4x^2-2x^2=-8-718 \\ \Leftrightarrow -6x^2 = -726 \\ \Leftrightarrow x^2 = \frac{-726}{-6}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
2. \(-8x^2+385=-6x^2-7 \\ \Leftrightarrow -8x^2+6x^2=-7-385 \\ \Leftrightarrow -2x^2 = -392 \\ \Leftrightarrow x^2 = \frac{-392}{-2}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
3. \(-4(-8x^2+7)=-(-31x^2+53) \\ \Leftrightarrow 32x^2-28=31x^2-53 \\ \Leftrightarrow 32x^2-31x^2=-53+28 \\ \Leftrightarrow x^2 = -25 \\ \Leftrightarrow x^2 = \frac{-25}{1} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-2(5x^2+10)=-(6x^2+344) \\ \Leftrightarrow -10x^2-20=-6x^2-344 \\ \Leftrightarrow -10x^2+6x^2=-344+20 \\ \Leftrightarrow -4x^2 = -324 \\ \Leftrightarrow x^2 = \frac{-324}{-4}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
5. \(3(8x^2+2)=-(-17x^2-1189) \\ \Leftrightarrow 24x^2+6=17x^2+1189 \\ \Leftrightarrow 24x^2-17x^2=1189-6 \\ \Leftrightarrow 7x^2 = 1183 \\ \Leftrightarrow x^2 = \frac{1183}{7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
6. \(-5x^2+180=0 \\ \Leftrightarrow -5x^2 = -180 \\ \Leftrightarrow x^2 = \frac{-180}{-5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
7. \(11x^2+6=10x^2-3 \\ \Leftrightarrow 11x^2-10x^2=-3-6 \\ \Leftrightarrow x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{1} < 0 \\ V = \varnothing \\ -----------------\)
8. \(5x^2-180=0 \\ \Leftrightarrow 5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
9. \(6x^2+426=9x^2-6 \\ \Leftrightarrow 6x^2-9x^2=-6-426 \\ \Leftrightarrow -3x^2 = -432 \\ \Leftrightarrow x^2 = \frac{-432}{-3}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
10. \(3(-2x^2-10)=-(2x^2+26) \\ \Leftrightarrow -6x^2-30=-2x^2-26 \\ \Leftrightarrow -6x^2+2x^2=-26+30 \\ \Leftrightarrow -4x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{-4} < 0 \\ V = \varnothing \\ -----------------\)
11. \(9x^2+3=7x^2+3 \\ \Leftrightarrow 9x^2-7x^2=3-3 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-4(-10x^2+8)=-(-39x^2-4) \\ \Leftrightarrow 40x^2-32=39x^2+4 \\ \Leftrightarrow 40x^2-39x^2=4+32 \\ \Leftrightarrow x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{1}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)