Question

Bai 1 : Tim gia tri nho nhat cua bieu thuc :

1, \(x^2-6x+6\)

2, \(3x^2-5x+2\)

3, \(5x^4+9x^2+13\)

4, \(x^2-5x+3\)

5, \(2x^2-5x-1\)

Answer 1

4.

= x\(^2\)-2.\(\dfrac{5}{2}\)x+\(\dfrac{25}{4}\)-\(\dfrac{13}{4}\)

= (x-\(\dfrac{5}{2}\))\(^2\)-\(\dfrac{13}{4}\)lớn hơn hoặc bằng -\(\dfrac{13}{4}\) với mọi x

=> min= -\(\dfrac{13}{4}\) <=> x = 5/2

Answer 2

5.

= 2( x\(^2\)-\(\dfrac{5}{2}\)x-\(\dfrac{1}{2}\))

=2( x\(^2\)-2.\(\dfrac{5}{4}\)+\(\dfrac{25}{4}\)-\(\dfrac{27}{4}\))

=2( x-\(\dfrac{5}{4}\))\(^2\)-\(\dfrac{27}{2}\) lớn hơn hoặc bằng -27/2 với mọi x

vậy min = -\(\dfrac{27}{2}\) <=> x= 5/4

Answer 3

1.

= x\(^2\)- 2.3x+9-3

= (x-3)\(^2\)-3 lớn hơn hoặc bằng -3 với mọi x

=> min = -3 <=> x=3

Answer 4

2.

= 3( x\(^2\)-2.\(\dfrac{5}{6}\)x+\(\dfrac{25}{36}\)-\(\dfrac{1}{36}\))

=3(x-\(\dfrac{5}{6}\))\(^2\)-\(\dfrac{1}{12}\)lớn hơn hoặc bằng -\(\dfrac{1}{12}\)với mọi x

=> min = -\(\dfrac{1}{12}\) <=> x= \(\dfrac{5}{6}\)