Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 229

2 problems

1
if

are integers
such that

show that
(a-d)²≥ 4d+8

2

find all real solutions to the equation

Last edited by tony123 (2007-12-27 11:06:39)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: 2 problems

x^5 + x^4-  x^3 - x^2 - x - 1 = 0
(x+1)(x^4-x^2-1)

x = -1

x^4 - x^2 - 1

x^2 = (1 +- sqrt(5))/2 = phi , 1-phi

x = +-√phi, +-√(1-phi)

x = -1, ±1.2720196495140689642524224617375, ±0.78615137775742328606955858584296i

so the reals are just the first 3

Last edited by luca-deltodesco (2007-12-27 11:19:41)

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