Question

Cho 2 số x,y dương thỏa mãn: \(x^2+x^2y^2-2y=x^3+2y^2-4y+3=0\)Tính giá trị của Q=\(x^2+y^2\)

Answer 1

Ta có:

\(x^2+x^2y^2-2y=0\)

\(\Leftrightarrow x^2=\frac{2y}{y^2+1}\le1\)(cái này chứng minh đơn giản b tự làm lấy nhé)

\(\Leftrightarrow-1\le x\le1\left(1\right)\)

Ta lại có:

\(x^3+2y^2-4y+3=0\)

\(\Leftrightarrow x^3=-1-2\left(y-1\right)^2\le-1\left(2\right)\)

Từ (1) và (2) \(\Rightarrow x=-1\)

\(\Rightarrow y=1\)

\(\Rightarrow x^2+y^2=1+1=2\)

Answer 2

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Answer 3

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Answer 6

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Answer 7

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Answer 8

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Answer 9

Bạn có thể giúp mik giải bài này đk chứ