For the square of quadratic binomial x-10x + 36, Xiao Cong made the following conclusion: no matter what number x takes, its value is not acceptable

For the square of quadratic binomial x-10x + 36, Xiao Cong made the following conclusion: no matter what number x takes, its value is not acceptable


The square of X - 10x + 36 = (X-5) ^ 2 + 11 ≥ 11
Conclusion: no matter what number x takes, its value cannot be less than 11



For the quadratic trinomial x ^ 2-10x + 36, Xiao Cong made the following conclusion: no matter what real number x takes, its value cannot be 10,
Do you agree with his statement and give reasons


There are two ways
Solution 1: let x ^ 2-10x + 36 = 10,
X^2-10X=-26
(X-5)^2=-26+25
(X-5)^2=-1,
On the left is the perfect square, which can't be negative,
The original quadratic trinomial cannot be equal to 10
Solution 2
x^2-10x+36=(X-5)^2+11≥10,
It can't be equal to 10
So I agree with Xiao Cong



For the square of quadratic trinomial x minus 10x plus 36, Xiao Bao made the following conclusion: no matter what real number x takes, its value will not be less than 11. Are you the same