\(A=9x^2+4y^2+54x-36y-12xy+90\)

\(A=\left(3x-2y\right)^2+18\left(3x-2y\right)+81+9\)

\(A=\left[\left(3x-2y\right)+9\right]^2+9\)

GTNN là 9 khi \(\left(3x-2y\right)+9=0\)

\(\Leftrightarrow\) \(3x=2y-9\)

\(\Leftrightarrow\) \(x=\dfrac{2y-9}{3}\)

\(\Leftrightarrow\) \(a=\dfrac{2}{3}\) và \(b=-3\)

à bổ sung thêm

Khi đó \(a+b=\dfrac{2}{3}+\left(-3\right)=\dfrac{-7}{3}\)

Thiếu 1 xíu thông cảm nha

\(A=\left(3x\right)^2+\left(2y\right)^2+81-12xy+2.\left(3x\right).9-2.\left(2y\right).9+9\)

\(A=\left(3x-2y+9\right)^2+9\ge9\)

\(\Rightarrow A_{min}=9\) khi \(3x-2y+9=0\Rightarrow3x=2y-9\Rightarrow x=\frac{2}{3}y-3\)

\(\Rightarrow\left\{{}\begin{matrix}a=\frac{2}{3}\\b=-3\end{matrix}\right.\)

A=9x² + 4y² + 54x − 36y − 12xy + 90

⟺A=9x²+4y²+81+54x−36y−12xy+9
⟺A=(3x−2y+9)2+9≥9⟺A=(3x−2y+9)2+9≥9

Dấu "=" xảy ra khi 3x−2y+9=0⟺x=2y / 3−33x−2y+9=0⟺x=2y3−3

Đối chiếu đề bài, ta suy ra a= 2  / 3, b=−3

Và a + b = 2 / 3 + -3 

8x−2x^2+5
= −2(x^2−4x−5/2)
= −2(x^2−4x+4−13/2)
= −2(x−2)^2+13≤13
=> GTLN là 13 khi x=2.

A=9x^2+4y^2+54x-36y-12xy+90 
A=(3x-2y)^2+18(3x-2y)+81+9 
A=[(3x-2y)+9]^2+9 
GTNN là 9 khi và chỉ khi (3x-2y)+9=0 
=>3x=2y-9 
=>x=(2y-9)/3 
Suy ra a=2/3 và b=-3 

tim minA khi X=.........,Y=............

the ket qua vao X=ay+b de tim a, b

\(\frac{x^2}{\left(2-x^2\right)x^2}=\frac{4x^2\left(2-x^2\right)}{\left(2-x^2\right)x^2}-\frac{4x\left(2-x^2\right)}{\left(2-x^2\right)x^2}+\frac{2-x^2}{\left(2-x^2\right)x^2}\)

\(\Leftrightarrow x^2=8x^2-4x^4-8x+4x^3+2x-x^2\)

\(\Leftrightarrow6x^2-4x^4+4x^3-6x=0\)

\(\Leftrightarrow4x^3\left(1-x\right)-6x\left(1-x\right)=0\)

\(\Leftrightarrow\left(4x^3-6x\right)\left(1-x\right)=0\)

\(\Leftrightarrow2x\left(2x^2-3\right)\left(1-x\right)=0\)