Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(5x^2-3)=-(-33x^2+1367)\)
2. \(-5(7x^2+6)=-(39x^2-114)\)
3. \(x^2-36=0\)
4. \(4(8x^2+4)=-(-33x^2-41)\)
5. \(6x^2-7=8x^2-9\)
6. \(-3x^2-79=-2x^2+2\)
7. \(3(7x^2-5)=-(-18x^2-348)\)
8. \(-5x^2+605=0\)
9. \(3x^2-474=7x^2+10\)
10. \(2x^2+258=6x^2+2\)
11. \(4x^2-16=0\)
12. \(-8x^2+12=-7x^2+3\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(5x^2-3)=-(-33x^2+1367) \\ \Leftrightarrow 25x^2-15=33x^2-1367 \\ \Leftrightarrow 25x^2-33x^2=-1367+15 \\ \Leftrightarrow -8x^2 = -1352 \\ \Leftrightarrow x^2 = \frac{-1352}{-8}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
2. \(-5(7x^2+6)=-(39x^2-114) \\ \Leftrightarrow -35x^2-30=-39x^2+114 \\ \Leftrightarrow -35x^2+39x^2=114+30 \\ \Leftrightarrow 4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
3. \(x^2-36=0 \\ \Leftrightarrow x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{1}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
4. \(4(8x^2+4)=-(-33x^2-41) \\ \Leftrightarrow 32x^2+16=33x^2+41 \\ \Leftrightarrow 32x^2-33x^2=41-16 \\ \Leftrightarrow -x^2 = 25 \\ \Leftrightarrow x^2 = \frac{25}{-1} < 0 \\ V = \varnothing \\ -----------------\)
5. \(6x^2-7=8x^2-9 \\ \Leftrightarrow 6x^2-8x^2=-9+7 \\ \Leftrightarrow -2x^2 = -2 \\ \Leftrightarrow x^2 = \frac{-2}{-2}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(-3x^2-79=-2x^2+2 \\ \Leftrightarrow -3x^2+2x^2=2+79 \\ \Leftrightarrow -x^2 = 81 \\ \Leftrightarrow x^2 = \frac{81}{-1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(3(7x^2-5)=-(-18x^2-348) \\ \Leftrightarrow 21x^2-15=18x^2+348 \\ \Leftrightarrow 21x^2-18x^2=348+15 \\ \Leftrightarrow 3x^2 = 363 \\ \Leftrightarrow x^2 = \frac{363}{3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
8. \(-5x^2+605=0 \\ \Leftrightarrow -5x^2 = -605 \\ \Leftrightarrow x^2 = \frac{-605}{-5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(3x^2-474=7x^2+10 \\ \Leftrightarrow 3x^2-7x^2=10+474 \\ \Leftrightarrow -4x^2 = 484 \\ \Leftrightarrow x^2 = \frac{484}{-4} < 0 \\ V = \varnothing \\ -----------------\)
10. \(2x^2+258=6x^2+2 \\ \Leftrightarrow 2x^2-6x^2=2-258 \\ \Leftrightarrow -4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{-4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
11. \(4x^2-16=0 \\ \Leftrightarrow 4x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{4}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(-8x^2+12=-7x^2+3 \\ \Leftrightarrow -8x^2+7x^2=3-12 \\ \Leftrightarrow -x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{-1}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)