Question

1.已知2^10=a^2=4^b,化简（a/4+b/5）*(a/4-b/5)-(a/4+b/5)^2,并求值.

Answer 1

2^10=a^2 (2^5)^2=a^2 a= ±2^5=±32

2^10=4^b 4^b=2^(2b) 2b=10 b=5

（a/4+b/5）*(a/4-b/5)-(a/4+b/5)^2

=(a/4)^2-(b/5)^2-(a/4)^2-ab/10-(b/5)^2

=-2b^2/25-ab/10

所以,-2-16 或-2+16

原式=-18或14