How can B & # 178; - 4B + 5 be reduced to (b-2) square + 1 The method and thinking of solving the problem

How can B & # 178; - 4B + 5 be reduced to (b-2) square + 1 The method and thinking of solving the problem

b²-4b+5
=b²-4b+4+1
=（b²-4b+4）+1
=（b-2）²+1
Idea: complete square formula: (a ± b) = A & # 178; ± 2Ab + B & # 178;

Solve inequality 1.2-x / x-4 ≥ 0.2.l5x-1l ≤ 9.3. - 3x ^ 2-11x-6 ≥ 0.4. (1 / 3) ^ 2x ＜ (1 / 3) ^ x ^ 2-8

4. Equivalent to 2x > x ^ 2-8 is x ^ 2 - 2x -- 8

Given: x2-3x-1 = 0, find: (1) the value of X-1 / x, (2) the value of x2 + 1 / x2
Given: x2-3x1 = 0, find: (1) the value of X-1 / x, (2) the value of x2 + 1 / x2

If x = 0, then the equation does not hold, so x! = 0
Because x2-3x-1 = 0. Divide both sides by X
x-3-1/x=0
So X-1 / x = 3
(2) Because X-1 / x = 3
So the square of both sides: (x-1 / x) (x-1 / x) = 9
x2+1/x2=11