Question

这个题帮忙看一下吧！

Answer 1

m^7 + n^7 = m^7 - (-n)^7 = (m+n)(m^6 - m^5*n + m^4*n^2 - m^3*n^3 + m^2*n^4 - m*n^5 + n^6)
= (m+n)[ (m^2 + n^2)^3 - 3m^2 *n^2(m^2 + n^2) - mn(m^4 + n^4) + m^2*n^2(m^2 + n^2) - (mn)^3 ]
= (m+n){[(m+n)^2 - 2mn]^3 - 3(mn)^2 * [(m+n)^2 - 2mn] - mn[(m^2 + n^2)^2 - 2m^2*n^2]
+ (mn)^2 *[(m+n)^2 - 2mn] - (mn)^3}
∵m^2 = m+1，n^2 - n - 1 = 0，∴m、n是一元二次方程x^2 - x - 1=0的两根，
∴m+n=1，mn=-1 ，m^2 + n^2 = 3
∴m^7 + n^7 = 1 *(27 - 3*3 + 7 + 3 + 1) = 28

追问

亲，是等于29噢