Toán Lớp 9: cho x+3y=1.cmr:x²+y²>=1/10
Giúp mình vs ạ
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Toán Lớp 9: cho x+3y=1.cmr:x²+y²>=1/10
Giúp mình vs ạ
Comments ( 1 )
GTLN: Áp dụng BĐT a^2 + b^2 ≥ 2ab
⇒ x^2 + 1 ≥ 2x ⇒ 2 x^2 ≥ 4x − 2
y^2 + 1 ≥ 2 y ⇒ 3y^2 ≥ 6y − 3
⇒ 2 x^2 + 3 y^2 ≥ 2 (2 x + 3 y) − 5
mà 2 x^2 + 3 y^2 ≤ 5 ⇒ 2 ( 2 x + 3 y ) − 5 ≤ 5 ⇒ 2 x + 3 y ≤ 5
Vậy Max A = 5 khi x = y = 1