Originally Posted by

**IoNForce** OK, just to let you know, I managed to solve it!

Here it is:

(t+1)^4 + [t + 5]^4 = 82

t+1 = p

p^4 + [p + 4]^4 = 82

p^4 + [p ^2+ 16 + 8p]^2 = 82

p^4 + p^4 + 64p^2 + 256 + 16^3 + 32 p^2 + 256p - 82 = 0

2p^4 + 16p^3 + 96 p^2 + 256 p + 174 = 0

p = -1 => p + 1 = 0 {The left side MUST b equal to the right side of the equation}

2p^3 (p+1) + 14p^2 (p+1) + 82 p (p+1) + 174 (p+1) = 0

(p+1)[2p^3 + 14p^2+ 82 p +174] = 0

p = -3 => p + 3 = 0 {The left side MUST b equal to the right side of the equation}

(p+1)[2p^2 (p+3) + 8p (p+3) + 58 (p+3) ] = 0

(p+1)(p+3) [2p^2 + 8p + 58] = 0

t1 + 1 = p1

t1 + 1 = -1

t1 = -2

t2 + 1 = p2

t2 + 1 = -3

t2 = -4

2p^2 + 8p + 58 = 0 |:2

p^2 + 4p + 29 = 0 => a = 1, b = 4, c = 29

p3,4 = [ -b +/- √( b^2 - 4ac ) ] / 2a

p3,4 = [ -4 +/- √( 16 - 116 ) ] / 2

p3,4 = 2(-2 +/- 5i) / 2

p3 = -2 + 5i

p4 = -2 - 5i