Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(-9x^2+10)=-(52x^2+797)\)
2. \(2x^2+576=-5x^2+9\)
3. \(8x^2-288=0\)
4. \(3x^2+588=0\)
5. \(-3(-8x^2-3)=-(-21x^2+498)\)
6. \(-5(-3x^2+8)=-(-10x^2+60)\)
7. \(5(2x^2+4)=-(-5x^2-1000)\)
8. \(14x^2-2=9x^2+3\)
9. \(-3(9x^2-10)=-(21x^2-324)\)
10. \(x^2-221=-5x^2-5\)
11. \(-2x^2+392=0\)
12. \(x^2-169=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(-9x^2+10)=-(52x^2+797) \\ \Leftrightarrow -45x^2+50=-52x^2-797 \\ \Leftrightarrow -45x^2+52x^2=-797-50 \\ \Leftrightarrow 7x^2 = -847 \\ \Leftrightarrow x^2 = \frac{-847}{7} < 0 \\ V = \varnothing \\ -----------------\)
2. \(2x^2+576=-5x^2+9 \\ \Leftrightarrow 2x^2+5x^2=9-576 \\ \Leftrightarrow 7x^2 = -567 \\ \Leftrightarrow x^2 = \frac{-567}{7} < 0 \\ V = \varnothing \\ -----------------\)
3. \(8x^2-288=0 \\ \Leftrightarrow 8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
4. \(3x^2+588=0 \\ \Leftrightarrow 3x^2 = -588 \\ \Leftrightarrow x^2 = \frac{-588}{3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-3(-8x^2-3)=-(-21x^2+498) \\ \Leftrightarrow 24x^2+9=21x^2-498 \\ \Leftrightarrow 24x^2-21x^2=-498-9 \\ \Leftrightarrow 3x^2 = -507 \\ \Leftrightarrow x^2 = \frac{-507}{3} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-5(-3x^2+8)=-(-10x^2+60) \\ \Leftrightarrow 15x^2-40=10x^2-60 \\ \Leftrightarrow 15x^2-10x^2=-60+40 \\ \Leftrightarrow 5x^2 = -20 \\ \Leftrightarrow x^2 = \frac{-20}{5} < 0 \\ V = \varnothing \\ -----------------\)
7. \(5(2x^2+4)=-(-5x^2-1000) \\ \Leftrightarrow 10x^2+20=5x^2+1000 \\ \Leftrightarrow 10x^2-5x^2=1000-20 \\ \Leftrightarrow 5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
8. \(14x^2-2=9x^2+3 \\ \Leftrightarrow 14x^2-9x^2=3+2 \\ \Leftrightarrow 5x^2 = 5 \\ \Leftrightarrow x^2 = \frac{5}{5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(-3(9x^2-10)=-(21x^2-324) \\ \Leftrightarrow -27x^2+30=-21x^2+324 \\ \Leftrightarrow -27x^2+21x^2=324-30 \\ \Leftrightarrow -6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{-6} < 0 \\ V = \varnothing \\ -----------------\)
10. \(x^2-221=-5x^2-5 \\ \Leftrightarrow x^2+5x^2=-5+221 \\ \Leftrightarrow 6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{6}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
11. \(-2x^2+392=0 \\ \Leftrightarrow -2x^2 = -392 \\ \Leftrightarrow x^2 = \frac{-392}{-2}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
12. \(x^2-169=0 \\ \Leftrightarrow x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)