Given x2-x-1 = 0, then the value of X4 + 2x + 1 / X5 is?

Given x2-x-1 = 0, then the value of X4 + 2x + 1 / X5 is?

X ^ 2-x-1 = 0 (x-1 / 2) ^ 2-5 / 4 = 0x-1 / 2 = 1 / 2 * radical 5 or X-1 / 2 = - 1 / 2 * radical 5x = 1 / 2 + 1 / 2 * radical 5 or x = 1 / 2-1 / 2 * radical 5 substitute the value of X into: x ^ 4 + 2x + 1 / X5 = (x + 1) ^ 2 + 2x + 1 / [x * (x + 1) ^ 2] = x ^ 2 + 2x + 1 + 2x + 1 / (x ^ 3 + 2x ^ 2 + x) = x + 1 + 4X + 1 / [x * (x + 1) + 2 (x + 1) + x] = 5x

If the algebraic formula X & # 178; + 4x-3 is changed into the form of (x-m) &# 178; + K, where m and K are constants, then M + K=

x²+4x-3
=x²+4x+4-7
=(x+2)²-7
∴m=-2
k=-7
∴m+k=-9

If the algebraic formula X & # 178; + 2bx + 4 is changed into the form of (x-m) &# 178; + K, where m and K are constants, then k-m=__
Maximum_____

The solution of X & # 178; + 2bx + 4 = (x + b) &# 178; - B & # 178; + 4 is: M = - BK = 4-b & # 178; so: K-M = 4-b & # 178; + B = - (B & # 178; - B + 1 / 4) + 1 / 4 + 4 = - (B-1 / 2) &# 178; + 17 / 4 when B = 1 / 2, the maximum value is: 17 / 4. Then K-M = - B & # 178; + B + 4__ 17/4__