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![](https://rs.olm.vn/images/avt/0.png?1311)
x (5x - 3) - x2 (x - 1) + x (x2 - 6x) - 10 + 3x
= 5x2 - 3x - x3 + x2 + x3 - 6x2 - 10 +3x
= - 10
![](https://rs.olm.vn/images/avt/0.png?1311)
bạn chỉ cần nhân phá ngoặc ra rồi ghép các hạng tử có cùng biến là xong
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(A=x^2+3x+4=\left(x+\dfrac{3}{2}\right)^2+\dfrac{7}{4}\ge\dfrac{7}{4}\)
\(minA=\dfrac{7}{4}\Leftrightarrow x=-\dfrac{3}{2}\)
b) \(B=2x^2-x+1=2\left(x-\dfrac{1}{4}\right)^2+\dfrac{7}{8}\ge\dfrac{7}{8}\)
\(minB=\dfrac{7}{8}\Leftrightarrow x=\dfrac{1}{4}\)
c) \(C=5x^2+2x-3=5\left(x+\dfrac{1}{5}\right)^2-\dfrac{16}{5}\ge-\dfrac{16}{5}\)
\(minC=-\dfrac{16}{5}\Leftrightarrow x=-\dfrac{1}{5}\)
d) \(D=4x^2+4x-24=\left(2x+1\right)^2-25\ge-25\)
\(minD=-25\Leftrightarrow x=-\dfrac{1}{2}\)
e) \(E=x^2+6x-11=\left(x+3\right)^2-20\ge-20\)
\(minE=-20\Leftrightarrow x=-3\)
f) \(G=\dfrac{1}{4}x^2+x-\dfrac{1}{3}=\left(\dfrac{1}{2}x+1\right)^2-\dfrac{4}{3}\ge-\dfrac{4}{3}\)
\(minG=-\dfrac{4}{3}\Leftrightarrow x=-2\)
\(A=x^2+3x+4=\left(x^2+3x+\dfrac{9}{4}\right)+\dfrac{7}{4}=\left(x+\dfrac{3}{2}\right)^2+\dfrac{7}{4}\)
Do \(\left(x+\dfrac{3}{2}\right)^2\ge0\forall x\)
\(\Rightarrow A=\left(x+\dfrac{3}{2}\right)^2+\dfrac{7}{4}\ge\dfrac{7}{4}\)
\(minA=\dfrac{7}{4}\Leftrightarrow x+\dfrac{3}{2}=0\Leftrightarrow x=-\dfrac{3}{2}\)
Mấy câu còn lại làm tương tự nhé em^^
![](https://rs.olm.vn/images/avt/0.png?1311)
A = ( 3x + 1 ) 2 + 12x - ( 3x + 5 ) 2+ 2( 6x + 3 )
=9x2+6x+1+12x-9x2-30x-25+12x+6
=(9x2-9x2)+(6x+12x-30x+12x)+1-25+6
=0+0+(-18)
=-18
A=(3x+1)2+12x-(3x+5)2+2(6x+3)
=9x2+6x+1+12x-(9x2+30x+25)+12x+6
=9x2+6x+1+12x-9x2-30x-25+12x+6
=60x-18
\(\Rightarrow\)đề sai 100%
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\left(x-1\right)^4-x^2\left(x^2+6\right)+4x\left(x^2+1\right)\)
\(A=x^4-4x^3+6x^2-4x+1-x^4-6x^2+4x^3+4x\)
\(A=\left(x^4-x^4\right)+\left(-4x^3+4x^3\right)+\left(6x^2-6x^2\right)+\left(-4x+4x\right)+1\)
\(A=1\)
Vậy biểu thức không phụ thuộc vào x
a/ E = 3x ( x – 2 ) + x ( 6 – 3x ) + 5
= \(3x^2-6x+6x-3x^2+5=5\)
b/ F = ( x + 2 ) ( x – 3 ) – ( x + 3 ) x – 4 )
= \(x^2-x-6-x^2-3x+4x+12=6\)