Question

chứng minh rằng 9x-x^2-25  x <0 với mọi x

Answer 1

`9x-x^2-25 < 0`

`<=>x^2-9x+25 > 0`

`<=>x^2-2x. 9/2+81/4+19/4 > 0`

`<=>(x-9/2)^2+19/4 > 0`

`<=>(x-9/2)^2 > -19/4`  (LĐ `AA x`)

Answer 2

9
x
−
x
2
−
25
<
0
⇔
x
2
−
9
x
+
25
>
0
⇔
x
2
−
2
x
.
9
2
+
81
4
+
19
4
>
0
⇔
(
x
−
9
2
)
2
+
19
4
>
0
⇔
(
x
−
9
2
)
2
>
−
19
4
  (LĐ  
∀
x
 )