Given that x2-4x + 1 = 0 (1), find x2 + 1 / X2 (2) if m n is the two real roots of the equation x? - 4x + 1 = 0, find the value of the algebraic formula 2m & # 178; + 4N & # 178; - 8N + 1. Kneel down and ask the second question, and the first question is OK. Yes, offer a reward directly

Given that x2-4x + 1 = 0 (1), find x2 + 1 / X2 (2) if m n is the two real roots of the equation x? - 4x + 1 = 0, find the value of the algebraic formula 2m & # 178; + 4N & # 178; - 8N + 1. Kneel down and ask the second question, and the first question is OK. Yes, offer a reward directly

This paper is going to be 178; (4x + 4x + 1 = 4xx + 1 = 4xx + 1 = 4xx + 1 / x = 4 (x + 1 / x) \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\+ 2Mn = 16 so M & # 178; + n & # 178; = 14

On the equation of X: x 2 - (M + 3) x + m + 3 = 0, one root is greater than 4, and the other root is less than 2
X2 is the square of X

Let f (x) = x ^ 2 - (M + 3) x + m + 3
If the equation has two unequal roots, then
The discriminant (3 + m) ^ 2-4 (3 + m) > 0 is M1
It is known that one root is greater than 4 and one root is less than 2
f(2)1
f(4)7/3
In conclusion, M > 7 / 3

If the root of the equation f (x) = x2 + ax + (A-3) = 0 is larger than 1 and smaller than 1, the value range of a can be obtained

This is a root distribution problem
If the corresponding value of F (1) is less than 0, since the opening is upward, there must be two, one larger than 1 and the other smaller than 1
So just
F (1) = 1 + A + A-3 < 0, i.e. a