[Risolto] Risolvi equazioni parametriche

1) 5*x^2 + (10*a + 1)*x + 5*a^2 - 1 = 0 ≡
≡ x^2 + (5*a + 1/5)*x + a^2 - 1/5 = 0 ≡
≡ (x + (5*a + 1/5)/2)^2 - ((5*a + 1/5)/2)^2 + a^2 - 1/5 = 0 ≡
≡ (x + (5*a + 1/5)/2)^2 = (525*a^2 + 50*a + 21)/100 ≡
≡ x + (5*a + 1/5)/2 = ± √(525*a^2 + 50*a + 21)/10 ≡
≡ x = - (5*a + 1/5)/2 ± √(525*a^2 + 50*a + 21)/10
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2) p(x, k) = 5*k*x^2 - 2*(k - 1) + 1/(5*k) =
= (k = 0) & (p(x, 0) indefinito)
oppure
= (k != 0) & (vedi oltre)
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* 5*k*x^2 - 2*(k - 1) + 1/(5*k) =
= 5*k*x^2 - (10*k^2 - 10*k - 1)/(5*k) =
= 5*k*(x^2 - (10*k^2 - 10*k - 1)/(25*k^2)) =
= 5*k*(x + √((10*k^2 - 10*k - 1)/(25*k^2)))*(x - √((10*k^2 - 10*k - 1)/(25*k^2)))
= 5*k*(x + √(- 1/k^2 - 10/k + 10)/5)*(x - √(- 1/k^2 - 10/k + 10)/5)