Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(-7x^2-9)=-(-27x^2+1149)\)
2. \(-6x^2+726=0\)
3. \(-x^2+605=-7x^2+5\)
4. \(-8x^2+800=0\)
5. \(-7x^2+1183=0\)
6. \(3(-6x^2+2)=-(25x^2+1366)\)
7. \(-13x^2+106=-9x^2+6\)
8. \(4(6x^2-6)=-(-31x^2+24)\)
9. \(7x^2-1183=0\)
10. \(-6x^2-294=0\)
11. \(-2(-4x^2-6)=-(-x^2-124)\)
12. \(-3x^2-1581=-10x^2-6\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(-7x^2-9)=-(-27x^2+1149) \\ \Leftrightarrow 21x^2+27=27x^2-1149 \\ \Leftrightarrow 21x^2-27x^2=-1149-27 \\ \Leftrightarrow -6x^2 = -1176 \\ \Leftrightarrow x^2 = \frac{-1176}{-6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
2. \(-6x^2+726=0 \\ \Leftrightarrow -6x^2 = -726 \\ \Leftrightarrow x^2 = \frac{-726}{-6}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
3. \(-x^2+605=-7x^2+5 \\ \Leftrightarrow -x^2+7x^2=5-605 \\ \Leftrightarrow 6x^2 = -600 \\ \Leftrightarrow x^2 = \frac{-600}{6} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-8x^2+800=0 \\ \Leftrightarrow -8x^2 = -800 \\ \Leftrightarrow x^2 = \frac{-800}{-8}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
5. \(-7x^2+1183=0 \\ \Leftrightarrow -7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
6. \(3(-6x^2+2)=-(25x^2+1366) \\ \Leftrightarrow -18x^2+6=-25x^2-1366 \\ \Leftrightarrow -18x^2+25x^2=-1366-6 \\ \Leftrightarrow 7x^2 = -1372 \\ \Leftrightarrow x^2 = \frac{-1372}{7} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-13x^2+106=-9x^2+6 \\ \Leftrightarrow -13x^2+9x^2=6-106 \\ \Leftrightarrow -4x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-4}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
8. \(4(6x^2-6)=-(-31x^2+24) \\ \Leftrightarrow 24x^2-24=31x^2-24 \\ \Leftrightarrow 24x^2-31x^2=-24+24 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(7x^2-1183=0 \\ \Leftrightarrow 7x^2 = 1183 \\ \Leftrightarrow x^2 = \frac{1183}{7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
10. \(-6x^2-294=0 \\ \Leftrightarrow -6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{-6} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-2(-4x^2-6)=-(-x^2-124) \\ \Leftrightarrow 8x^2+12=x^2+124 \\ \Leftrightarrow 8x^2-x^2=124-12 \\ \Leftrightarrow 7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
12. \(-3x^2-1581=-10x^2-6 \\ \Leftrightarrow -3x^2+10x^2=-6+1581 \\ \Leftrightarrow 7x^2 = 1575 \\ \Leftrightarrow x^2 = \frac{1575}{7}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)