. the minimum value of the square of 3x + 6 / X (x > 0)

. the minimum value of the square of 3x + 6 / X (x > 0)

The cube root of 3x & # 178; + 3 / x + 3 / X ≥ 3 (3x & # 178; * 3 / X * 3 / x) = 9
So the minimum value is 9

Given the square of x-3x + 1 = 0, find the value under the root sign (square of X + 1 / square of x-1)

∵x²-3x+1=0
∴x≠0.
Divide both sides of the above equation by X
x+(1/x)=3
The formula is square on both sides
x²+(1/x²)+2=9
∴x²+(1/x²)=7
∴x²+(1/x²)-1=6
∴√[x²+(1/x²)-1]=√6

Let P (x, y) be a point on the ellipse X29 + y24 = 1, then the maximum value of 2x-y is___ ．

Let 2x-y = a, simultaneous equations y = 2x-a4x2 + 9y2 = 36, eliminate y, and sort out, get 40x2-36ax + 9a2-36 = 0, ■ △ = - A2 + 40 ≥ 0, ■ - 210 ≤ a ≤ 210, so the answer is: 210