Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(6x^2-10)=-(-16x^2-1760)\)
2. \(2x^2+32=0\)
3. \(5x^2-45=0\)
4. \(-3x^2+0=0\)
5. \(-3x^2+27=0\)
6. \(3x^2-6=2x^2-6\)
7. \(9x^2+893=5x^2-7\)
8. \(-3x^2-18=3x^2+6\)
9. \(-8x^2+283=-6x^2-5\)
10. \(-5x^2-1363=2x^2+9\)
11. \(-4x^2-11=-3x^2-2\)
12. \(3(4x^2-3)=-(-17x^2-971)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(6x^2-10)=-(-16x^2-1760) \\ \Leftrightarrow 24x^2-40=16x^2+1760 \\ \Leftrightarrow 24x^2-16x^2=1760+40 \\ \Leftrightarrow 8x^2 = 1800 \\ \Leftrightarrow x^2 = \frac{1800}{8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
2. \(2x^2+32=0 \\ \Leftrightarrow 2x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{2} < 0 \\ V = \varnothing \\ -----------------\)
3. \(5x^2-45=0 \\ \Leftrightarrow 5x^2 = 45 \\ \Leftrightarrow x^2 = \frac{45}{5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
4. \(-3x^2+0=0 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(-3x^2+27=0 \\ \Leftrightarrow -3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{-3}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
6. \(3x^2-6=2x^2-6 \\ \Leftrightarrow 3x^2-2x^2=-6+6 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(9x^2+893=5x^2-7 \\ \Leftrightarrow 9x^2-5x^2=-7-893 \\ \Leftrightarrow 4x^2 = -900 \\ \Leftrightarrow x^2 = \frac{-900}{4} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-3x^2-18=3x^2+6 \\ \Leftrightarrow -3x^2-3x^2=6+18 \\ \Leftrightarrow -6x^2 = 24 \\ \Leftrightarrow x^2 = \frac{24}{-6} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-8x^2+283=-6x^2-5 \\ \Leftrightarrow -8x^2+6x^2=-5-283 \\ \Leftrightarrow -2x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-2}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
10. \(-5x^2-1363=2x^2+9 \\ \Leftrightarrow -5x^2-2x^2=9+1363 \\ \Leftrightarrow -7x^2 = 1372 \\ \Leftrightarrow x^2 = \frac{1372}{-7} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-4x^2-11=-3x^2-2 \\ \Leftrightarrow -4x^2+3x^2=-2+11 \\ \Leftrightarrow -x^2 = 9 \\ \Leftrightarrow x^2 = \frac{9}{-1} < 0 \\ V = \varnothing \\ -----------------\)
12. \(3(4x^2-3)=-(-17x^2-971) \\ \Leftrightarrow 12x^2-9=17x^2+971 \\ \Leftrightarrow 12x^2-17x^2=971+9 \\ \Leftrightarrow -5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{-5} < 0 \\ V = \varnothing \\ -----------------\)