The minimum value of function y = x2 + 2 / X-1 (x > 1) is (basic inequality)

The minimum value of function y = x2 + 2 / X-1 (x > 1) is (basic inequality)

Because y = x & # 178; + 2 / X-1
So x & # 178; + 2 / X ≥ 2 √ 2x
So y = x & # 178; + 2 / X-1 ≥ 2 √ 2x-1
When x = 1, take the minimum value y = 2 √ 2-1

Using basic inequality to find the maximum value of y = x / x2 + 2
First find 1 / y = x + 2 / X
When x is less than 0, 1 / y = - (- X - 2 / x) is less than or equal to - 2 radical 2
The result is y less than or equal to - root 2 / 4, but the answer is greater than or equal to - root 2 / 4
Isn't it the same division minus sign? What's wrong with me

Answer:
xy≥1/(-2√2)
That is - √ 2 / 4 ≤ y

X2 + Y2 + Z2 is greater than or equal to x2 + (y + x) 2 / 2 (2 are square). Please explain why the inequality holds
The last two is not square

Is your second formula wrong
It should be x ^ 2 + (y + Z) ^ 2 / 2
The comparison is actually 2 (y ^ 2 + Z ^ 2) and (y + Z) ^ 2
The difference between the two formulas is that the square term of (Y-Z) ^ 2 is obviously greater than or equal to 0
Immediate evidence