Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(9x^2-2=3x^2-2\)
2. \(x^2-188=-3x^2+8\)
3. \(2x^2-72=0\)
4. \(-18x^2+285=-10x^2-3\)
5. \(2(5x^2+10)=-(-2x^2-532)\)
6. \(8x^2-1800=0\)
7. \(4x^2-4=0\)
8. \(5x^2+162=6x^2-7\)
9. \(-3x^2-110=-4x^2-10\)
10. \(3(5x^2+6)=-(-11x^2-694)\)
11. \(-3x^2-363=0\)
12. \(11x^2+479=7x^2-5\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(9x^2-2=3x^2-2 \\ \Leftrightarrow 9x^2-3x^2=-2+2 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(x^2-188=-3x^2+8 \\ \Leftrightarrow x^2+3x^2=8+188 \\ \Leftrightarrow 4x^2 = 196 \\ \Leftrightarrow x^2 = \frac{196}{4}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
3. \(2x^2-72=0 \\ \Leftrightarrow 2x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{2}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
4. \(-18x^2+285=-10x^2-3 \\ \Leftrightarrow -18x^2+10x^2=-3-285 \\ \Leftrightarrow -8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
5. \(2(5x^2+10)=-(-2x^2-532) \\ \Leftrightarrow 10x^2+20=2x^2+532 \\ \Leftrightarrow 10x^2-2x^2=532-20 \\ \Leftrightarrow 8x^2 = 512 \\ \Leftrightarrow x^2 = \frac{512}{8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
6. \(8x^2-1800=0 \\ \Leftrightarrow 8x^2 = 1800 \\ \Leftrightarrow x^2 = \frac{1800}{8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
7. \(4x^2-4=0 \\ \Leftrightarrow 4x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
8. \(5x^2+162=6x^2-7 \\ \Leftrightarrow 5x^2-6x^2=-7-162 \\ \Leftrightarrow -x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{-1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
9. \(-3x^2-110=-4x^2-10 \\ \Leftrightarrow -3x^2+4x^2=-10+110 \\ \Leftrightarrow x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
10. \(3(5x^2+6)=-(-11x^2-694) \\ \Leftrightarrow 15x^2+18=11x^2+694 \\ \Leftrightarrow 15x^2-11x^2=694-18 \\ \Leftrightarrow 4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
11. \(-3x^2-363=0 \\ \Leftrightarrow -3x^2 = 363 \\ \Leftrightarrow x^2 = \frac{363}{-3} < 0 \\ V = \varnothing \\ -----------------\)
12. \(11x^2+479=7x^2-5 \\ \Leftrightarrow 11x^2-7x^2=-5-479 \\ \Leftrightarrow 4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{4} < 0 \\ V = \varnothing \\ -----------------\)