Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3(-3x^2-10)=-(x^2+318)\)
2. \(-8x^2+1568=0\)
3. \(-4x^2-167=-3x^2+2\)
4. \(2x^2+72=0\)
5. \(-11x^2+1132=-6x^2+7\)
6. \(7x^2+7=2x^2+7\)
7. \(3(7x^2-7)=-(-13x^2+21)\)
8. \(-8x^2+8=0\)
9. \(2x^2-56=4x^2-6\)
10. \(-4x^2+0=0\)
11. \(-15x^2+347=-8x^2+4\)
12. \(-4x^2+64=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3(-3x^2-10)=-(x^2+318) \\ \Leftrightarrow -9x^2-30=-x^2-318 \\ \Leftrightarrow -9x^2+x^2=-318+30 \\ \Leftrightarrow -8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
2. \(-8x^2+1568=0 \\ \Leftrightarrow -8x^2 = -1568 \\ \Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
3. \(-4x^2-167=-3x^2+2 \\ \Leftrightarrow -4x^2+3x^2=2+167 \\ \Leftrightarrow -x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{-1} < 0 \\ V = \varnothing \\ -----------------\)
4. \(2x^2+72=0 \\ \Leftrightarrow 2x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{2} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-11x^2+1132=-6x^2+7 \\ \Leftrightarrow -11x^2+6x^2=7-1132 \\ \Leftrightarrow -5x^2 = -1125 \\ \Leftrightarrow x^2 = \frac{-1125}{-5}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
6. \(7x^2+7=2x^2+7 \\ \Leftrightarrow 7x^2-2x^2=7-7 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(3(7x^2-7)=-(-13x^2+21) \\ \Leftrightarrow 21x^2-21=13x^2-21 \\ \Leftrightarrow 21x^2-13x^2=-21+21 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(-8x^2+8=0 \\ \Leftrightarrow -8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(2x^2-56=4x^2-6 \\ \Leftrightarrow 2x^2-4x^2=-6+56 \\ \Leftrightarrow -2x^2 = 50 \\ \Leftrightarrow x^2 = \frac{50}{-2} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-4x^2+0=0 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-15x^2+347=-8x^2+4 \\ \Leftrightarrow -15x^2+8x^2=4-347 \\ \Leftrightarrow -7x^2 = -343 \\ \Leftrightarrow x^2 = \frac{-343}{-7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
12. \(-4x^2+64=0 \\ \Leftrightarrow -4x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)