Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(9x^2-178=8x^2-9\)
2. \(-3(-5x^2+6)=-(-11x^2+214)\)
3. \(-2(-8x^2-2)=-(-11x^2-4)\)
4. \(-3x^2-300=0\)
5. \(6x^2+216=0\)
6. \(-2x^2-162=0\)
7. \(4x^2-900=0\)
8. \(x^2+4=0\)
9. \(3(2x^2-4)=-(0x^2+1188)\)
10. \(-3(6x^2+8)=-(25x^2+24)\)
11. \(14x^2-1564=6x^2+4\)
12. \(7x^2+1008=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(9x^2-178=8x^2-9 \\ \Leftrightarrow 9x^2-8x^2=-9+178 \\ \Leftrightarrow x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
2. \(-3(-5x^2+6)=-(-11x^2+214) \\ \Leftrightarrow 15x^2-18=11x^2-214 \\ \Leftrightarrow 15x^2-11x^2=-214+18 \\ \Leftrightarrow 4x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{4} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-2(-8x^2-2)=-(-11x^2-4) \\ \Leftrightarrow 16x^2+4=11x^2+4 \\ \Leftrightarrow 16x^2-11x^2=4-4 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-3x^2-300=0 \\ \Leftrightarrow -3x^2 = 300 \\ \Leftrightarrow x^2 = \frac{300}{-3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(6x^2+216=0 \\ \Leftrightarrow 6x^2 = -216 \\ \Leftrightarrow x^2 = \frac{-216}{6} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-2x^2-162=0 \\ \Leftrightarrow -2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{-2} < 0 \\ V = \varnothing \\ -----------------\)
7. \(4x^2-900=0 \\ \Leftrightarrow 4x^2 = 900 \\ \Leftrightarrow x^2 = \frac{900}{4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
8. \(x^2+4=0 \\ \Leftrightarrow x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{1} < 0 \\ V = \varnothing \\ -----------------\)
9. \(3(2x^2-4)=-(0x^2+1188) \\ \Leftrightarrow 6x^2-12=0x^2-1188 \\ \Leftrightarrow 6x^2+0x^2=-1188+12 \\ \Leftrightarrow 6x^2 = -1176 \\ \Leftrightarrow x^2 = \frac{-1176}{6} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-3(6x^2+8)=-(25x^2+24) \\ \Leftrightarrow -18x^2-24=-25x^2-24 \\ \Leftrightarrow -18x^2+25x^2=-24+24 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(14x^2-1564=6x^2+4 \\ \Leftrightarrow 14x^2-6x^2=4+1564 \\ \Leftrightarrow 8x^2 = 1568 \\ \Leftrightarrow x^2 = \frac{1568}{8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
12. \(7x^2+1008=0 \\ \Leftrightarrow 7x^2 = -1008 \\ \Leftrightarrow x^2 = \frac{-1008}{7} < 0 \\ V = \varnothing \\ -----------------\)