\(A=\frac{3\left(x^2-4x+5\right)-5}{x^2-4+5}=3-\frac{5}{\left(x-2\right)^2+1}\ge3-5=-2\)

Dau '=' xay ra khi \(x=2\)

Vay \(A_{min}=-2\)khi \(x=2\)

a) Ta có: \(A=3x^2-6x+5\)

\(=3\left(x^2-2x+\frac{5}{3}\right)\)

\(=3\left(x^2-2x+1+\frac{2}{3}\right)\)

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

Ta có: \(\left(x-1\right)^2\ge0\forall x\)

\(\Rightarrow3\left(x-1\right)^2\ge0\forall x\)

\(\Rightarrow3\left(x-1\right)^2+2\ge2\forall x\)

Dấu '=' xảy ra khi x-1=0

hay x=1

Vậy: Giá trị nhỏ nhất của biểu thức \(A=3x^2-6x+5\) là 2 khi x=1

b) Ta có: \(4x^2-12x+35\)

\(=4\left(x^2-3x+\frac{35}{4}\right)\)

\(=4\left(x^2-2\cdot x\cdot\frac{3}{2}+\frac{9}{4}+\frac{26}{4}\right)\)

\(=4\left(x-\frac{3}{2}\right)^2+26\)

Ta có: \(\left(x-\frac{3}{2}\right)^2\ge0\forall x\)

\(\Rightarrow4\left(x-\frac{3}{2}\right)^2\ge0\forall x\)

\(\Rightarrow4\left(x-\frac{3}{2}\right)^2+26\ge26\forall x\)

\(\Rightarrow4x^2-12x+35\ge26\forall x\)

\(\Rightarrow\frac{5}{4x^2-12x+35}\le\frac{5}{26}\forall x\)

\(\Rightarrow\frac{-5}{4x^2-12x+35}\ge\frac{-5}{26}\forall x\)

Dấu '=' xảy ra khi \(x-\frac{3}{2}=0\)

hay \(x=\frac{3}{2}\)

Vậy: Giá trị nhỏ nhất của biểu thức \(B=-\frac{5}{4x^2-12x+35}\) là \(-\frac{5}{26}\) khi \(x=\frac{3}{2}\)

a) 5.(x^2-3x+1)+x.(1-5x)=x-2

\(\Leftrightarrow5x^2-15x+5+x-5x^2=x-2\)

\(\Leftrightarrow-14x-x=-2-5\)

\(\Leftrightarrow-15x=-7\)

\(\Leftrightarrow x=\frac{7}{15}\)

b\(,3x.\left(\frac{4}{3}+1\right)-4x\left(x-2\right)=10\)

\(\Leftrightarrow4x+3x-4x^2+8x-10=0\)

\(\Leftrightarrow-4x^2+15x-10=0\)

Đề sai???

\(c,12x^2-4x\left(3x-5\right)=10x-17\)

\(\Leftrightarrow12x^2-12x^2+20x-10x=-17\)

\(\Leftrightarrow10x=-17\)

\(\Leftrightarrow x=-\frac{17}{10}\)

\(d,4x\left(x-5\right)-7x\left(x-4\right)+3x^2=12\)

\(\Leftrightarrow4x^2-20x-7x^2+28x+3x^2=12\)

\(\Leftrightarrow8x=12\)

\(\Leftrightarrow x=\frac{3}{2}\)

\(a,5\left(x^2-3x+1\right)+x\left(1-5x\right)=x-2\)

\(\Leftrightarrow5x^2-15x+5+x-5x^2-x+2=0\)

\(\Leftrightarrow-15x+7=0\)

\(\Leftrightarrow-15x=-7\)

\(\Leftrightarrow x=-\frac{7}{-15}\)

\(\Leftrightarrow x=\frac{7}{15}\)

\(A=x^2-6x+10\)

\(\Leftrightarrow A=x^2-2\cdot x\cdot3+3^2-9+10\)

\(\Leftrightarrow A=\left(x-3\right)^2+1\ge1\)     \(\forall x\in z\)

\(\Leftrightarrow A_{min}=1khix=3\)

\(B=3x^2-12x+1\)

\(\Leftrightarrow B=\left(\sqrt{3}x\right)^2-2\cdot\sqrt{3}x\cdot2\sqrt{3}+\left(2\sqrt{3}\right)^2-12+1\)

\(\Leftrightarrow B=\left(\sqrt{3}x-2\sqrt{3}\right)^2-11\ge-11\)    \(\forall x\in z\)

\(\Leftrightarrow B_{min}=-11khix=2\)

làm khuyến mại 1 câu;

a) = 12x² -12x² +20x -10x +17 =0

10x = -17

x = -17/10

x/2 - ( 3x/5 - 13/5 ) = -( 7/5 + 7/10x )

a) = 12x2 -12x2 +20x -10x +17 =0

10x = -17

x = -17/10