TA CÓ (2X + 4Y)2 + ( 4X – 2Y)2 = 4X2+ 16Y2 +16XY + 16X2 + 4Y2 –16XY =...

câu 3: - DE THI HSG TOAN 9 FULL DAP AN
DE THI HSG TOAN 9 FULL DAP AN
Câu 3: Ta có (2x + 4y)

2

+ ( 4x – 2y)

2

= 4x

2

+ 16y

2

+16xy + 16x

2

+ 4y

2

–16xy = 20(x

2

+y

2

) Biết rằng (2x + 4y)

2

+ (4x – 2y)

2

≥

(2x +4y)

2

Dấu “=” xảy ra

⇔

4x – 2y = 0

⇔

y = 2x

⇒

20(x

2

+ y

2

)

≥

1 (do 2x +4y = 1)

1

⇒

A = x

2

+ y

2

≥

20

1

=

y



2

y

x

1

⇔

5

⇔

⇒

min A =

+

4

10