Let t = a 2-ab+b 2 = 1-2ab.

When ab>0, it is easy to know that the minimum value of t can be found.

Because 1 = A 2+AB+B 2 > =2ab+ab.

Then ab < = 1/3

So t> =1-2 *1/3 =1/3.

When ab

1=a^2+ab+b^2>； =(-2ab)+ab

ab & gt=- 1

So t =

therefore

1/3 & lt； = t & lt=3

2、

From the question 2007 * a 2 = 2008 * b 2, (2 refers to the square)

Know (A/B) 2 = 2008/2007, and in the same way (B/A) 2 = 2007/2008.

Then 1/a+ 1/b= 1, (it should be a >；; 0, b>0, I understand it this way)

So we know

A/b= under the root symbol (2008/2007), similarly b/a= under the root symbol (2007/2008).

Multiply both sides by a to get 1+a/b=a,

Therefore, under the root sign of a= 1+ (2008/2007),

In the same way, multiply both sides by b to get it

B =1+under the root symbol (2007/2008)

replace

(2007a+2008b)

=2007*[ 1+ root number (2008/2007)]

=2007+2008+2007* under the root number (2008/2007)+2008* under the root number (2007/2008)

=2007+2008+ number of roots (2007*2008)+ number of roots (2007*2008)

=50 15+2* under the root symbol (2007*2008)

= = Root number of 2007+2 * (2007 * 2008) +2008

= (root number 2007+ root number 2008) squared.

therefore

Under the root number (2007a+2008b)

= number of roots 2007+ number of roots 2008