5Q^6-21Q^4+16=0会的快回一下

Question

5Q^6-21Q^4+16=0
会的快回一下

Answer 1

5Q^6 -21Q^4 +16 =0
5Q^6 -5Q^4 -16Q^4 +16 =0
5Q^4(Q^2 -1) -16(Q^4 -1) =0
5Q^4(Q^2-1) -16(Q^2+1)(Q^2-1) =0
(Q^2-1)(5Q^4-16(Q^2+1)) =0
(Q^2-1)(5Q^4-16Q^2-16) =0
(Q^2-1)(5Q^2+4)(Q^2-4) =0
因为(5Q^2+4)不可能为0,
所以,(Q^2-1) =0,(Q^2-4) = 0
所以,
方程的解为：
Q1 = 1,Q2 = -1,Q3 = 2,Q4 = -2.