a/ ĐKXĐ: \(\left\{{}\begin{matrix}2x+1\ge0\\3\left|x\right|^2+5\left|x\right|-2\ne0\\x-\left|x\right|\ne0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x\ge-\frac{1}{2}\\\left|x\right|\ne\frac{1}{3}\\x< 0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}-\frac{1}{2}\le x< 0\\x\ne-\frac{1}{3}\end{matrix}\right.\)

b/ Nếu \(x\in D\Rightarrow-x\in D\)

\(f\left(-x\right)=\frac{\left|-2017x-10\right|-\left|-2017x+10\right|}{x^6-8x^4+16x^2}\)

\(=\frac{\left|2017x+10\right|-\left|2017x-10\right|}{x^6-8x^4+16x^2}=-\frac{\left|2017x-10\right|-\left|2017x+10\right|}{x^6-8x^4+16x^2}=-f\left(x\right)\)

Hàm lẻ

Câu c) Sử dụng hằng đẳng thức+Đặt biến phụ

Ta có: \(x^2+2xy+y^2-x-y-12\)

\(=\left(x+y\right)^2-\left(x+y\right)-12\)

\(=\left(x+y\right)\left(x+y-1\right)-12\)

Đặt: \(x+y=t\)

\(=t\left(t-1\right)-12\)

\(=t^2-t-12\)

\(=t^2-t-9-3\)

\(=\left(t^2-3^2\right)-\left(t+3\right)\)

\(=\left(t+3\right)\left(t-3\right)-\left(t+3\right)\)

\(=\left(t+3\right)\left(t-4\right)\)Bn tự thế vào nhá. (Bài c) tương tự bài a))

Câu d) Đặt biến phụ

Ta có: \(\left(5x^2-2x\right)^2+2x-5x^2-6\)

\(=\left(5x^2-2x\right)^2-5x^2+2x-6\)

\(=\left(5x^2-2x\right)^2-\left(5x^2-2x\right)-6\)

\(=\left(5x^2-2x\right)\left(5x^2-2x-1\right)-6\)

Đặt \(t=5x^2-2x\)

\(=t\left(t-1\right)-6\)

\(=t^2-t-6\)

\(=t^2-t-9+3\)

\(=\left(t^2-3^2\right)-\left(t-3\right)\)

\(=\left(t-3\right)\left(t+3\right)-\left(t-3\right)\)

\(=\left(t-3\right)\left(t+2\right)\)Bn tự thế t vào 

Câu a) Sử dụng phương pháp đặt biến phụ+hằng đẳng thức

Ta có: \(\left(2x^2+x-2\right)\left(2x^2+x-3\right)-12\)

Đặt: \(t=2x^2+x-2\)

\(=t\left(t-1\right)-12\)

\(=t^2-t-12=t^2-t-9-3\)

\(=\left(t^2-3^2\right)-\left(t+3\right)\)

\(\left(t+3\right)\left(t-3\right)-\left(t+3\right)=\left(t+3\right)\left(t-4\right)\)

Thay t vào: \(\left(2x^2+x+1\right)\left(2x^2+x-6\right)\)

Câu b) Sử dụng hằng đẳng thức+ đặt biến phụ 

Ta có: \(x^2+9y^2-9y-3x+6xy+2\)

\(=\left(x^2+6xy+9y^2\right)-\left(9y+3x\right)+2\)

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

\(=\left(x+3y\right)\left(x+3y-3\right)+2\)

Đặt \(t=x+3y\)

\(=t\left(t-3\right)+2\)

\(=t^2-3t+2\)

\(=\left(t^2-4\right)-\left(3t-6\right)\)

\(=\left(t-2\right)\left(t+2\right)-3\left(t-2\right)\)

\(=\left(t-2\right)\left(t-1\right)\)Khúc sau bn tự thế vào

Còn mấy bài sau đang nghiên cứu

f) Câu nầy suy nghĩ muốn chết mới ra

Ta có: \(x^4+2018x^2+2017x+2018\)

\(=\left(x^4-x\right)+\left(2018x^2+2018x+2018\right)\)

\(=x\left(x^3-1\right)+2018\left(x^2+x+1\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+2018\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2018\right)\)

e) Tương tự như câu f) 

Ta có: \(x^4+2018x^2-2017x+2018\)

\(=\left(x^4+x\right)\left(2018x^2-2018+2018\right)\)

\(=x\left(x^3+1\right)+2018\left(x^2-x+1\right)\)

\(=x\left(x+1\right)\left(x^2-x+1\right)+2018\left(x^2-x+1\right)\)

\(=\left(x^2-x+1\right)\left(x^2+x+2018\right)\)

g) Tương tự như hai câu trên

Ta có: \(x^4-30x^2+31x-30\)

\(=x^4-30x^2+30x+x-30\)

\(=\left(x^4+x\right)-\left(30x^2-30x+30\right)\)

\(=x\left(x^3+1\right)-30\left(x^2-x+1\right)\)

\(=x\left(x+1\right)\left(x^2-x+1\right)-30\left(x^2-x+1\right)\)

\(=\left(x^2-x+1\right)\left(x^2+x-30\right)\)

Ta có  

\(\left(\sqrt{27+10\sqrt{2}}-\sqrt{27-10\sqrt{2}}\right)^2\)

\(=27+10\sqrt{2}+27-10\sqrt{2}-2\sqrt{\left(27+10\sqrt{2}\right)\left(27-10\sqrt{2}\right)}\)

\(=54-2\sqrt{529}=8\)

\(\Rightarrow\)  \(\sqrt{27+10\sqrt{2}}-\sqrt{27-10\sqrt{2}}=\sqrt{8}=2\sqrt{2}\)

Xét tử số

\(\left(27+10\sqrt{2}\right)\sqrt{27-10\sqrt{2}}-\left(27-10\sqrt{2}\right)\sqrt{27+10\sqrt{2}}\)

\(=\left(\sqrt{27+10\sqrt{2}}.\sqrt{27-10\sqrt{2}}\right)\left(\sqrt{27+10\sqrt{2}}-\sqrt{27-10\sqrt{2}}\right)\)

\(=23\left(\sqrt{27+10\sqrt{2}}-\sqrt{27-10\sqrt{2}}\right)\)

\(=23.2\sqrt{2}=46\sqrt{2}\)

Lại có  \(\left(\sqrt{\sqrt{13}-3}+\sqrt{\sqrt{13}+3}\right)^2\)

\(=\sqrt{13}-3+\sqrt{13}+3+2\sqrt{\left(\sqrt{13}-3\right)\left(\sqrt{13}+3\right)}\)

\(=2\sqrt{13}+2\sqrt{4}=2\sqrt{13}+4\)

ta bình phương mẫu số

\(\left(\frac{\sqrt{\sqrt{13}-3}+\sqrt{\sqrt{13}+3}}{\sqrt{\sqrt{13}+2}}\right)^2=\frac{\left(\sqrt{\sqrt{13}-3}+\sqrt{\sqrt{13}+3}\right)^2}{\sqrt{13}+2}\)

\(=\frac{2\sqrt{13}+4}{\sqrt{13}+2}=2\)

Vậy mẫu  \(=\sqrt{2}\)

Vậy  \(x=\frac{46\sqrt{2}}{\sqrt{2}}=46\)  thay vào ta đc A = 92880

4036

4036

dam cong tian Làm giúp đi mk bó tay cái dạng này !! -_-

\(5x^2+5y^2+8xy-2x+2y+2=0\)

\(\Leftrightarrow4\left(x+y\right)^2+\left(x-1\right)^2+\left(y+1\right)^2=0\)

Vì \(\left(x+y\right)^2\ge0,\left(x-1\right)^2\ge0,\left(y+1\right)^2\ge0\)

\(\Rightarrow4\left(x+y\right)^2+\left(x-1\right)^2+\left(y+1\right)^2\ge0\)

Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}x+y=0\\x-1=0\\y+1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-1\end{matrix}\right.\)

\(\left(x+y\right)^{2018}+\left(x-2\right)^{2019}+\left(y+1\right)^{2020}=\left(1-1\right)^{2018}+\left(1-2\right)^{2019}+\left(-1+1\right)^{2020}=-1\)

bạn tải ảnh về r up lại đi bạn

\(a,4\left(x-3\right)^2-\left(2x-1\right)^2\ge12\)

\(\Leftrightarrow4x^2-24x+36-4x^2-4x+1\ge12\)

\(\Leftrightarrow-28x+37\ge12\)

\(\Leftrightarrow-28x\ge12-37\)

\(\Leftrightarrow-28x\ge-25\)

\(\Leftrightarrow x\le\dfrac{25}{28}\)

Vậy \(S=\left\{x\left|x\le\dfrac{25}{28}\right|\right\}\)

b, \(\left(x-4\right)\left(x+4\right)\ge\left(x+3\right)^2+5\)

\(\Leftrightarrow x^2-16\ge x^2+6x+9+5\)

\(\Leftrightarrow x^2-x^2-6x\ge9+5+16\)

\(\Leftrightarrow-6x\ge30\)

\(\Leftrightarrow x\le-5\)

Vậy \(S=\left\{x\left|x\le-5\right|\right\}\)

\(c,\left(3x-1\right)^2-9\left(x+2\right)\left(x-2\right)< 5x\)

\(\Leftrightarrow9x^2-6x-1-9x^2+36< 5x\)

\(\Leftrightarrow9x^2-9x^2-6x-5x+36+1< 0\)

\(\Leftrightarrow-11x+37< 0\)

\(\Leftrightarrow-11x< -37\)

\(\Leftrightarrow x>\dfrac{37}{11}\)

vậy \(S=\left\{x\left|x>\dfrac{37}{11}\right|\right\}\)

2x² + 2y² + 3xy - x + y + 1 = 0

2x² + 2y² + 4xy - xy - x + y + 1 = 0

(2x² + 2y² + 4xy) + (-xy - x) + (y + 1) = 0

2(x + y)² - x(y + 1) + (y + 1) = 0

2(x + y)² + (y + 1)(1 - x) = 0

Do (x + y)² \(\ge0\)

\(\Rightarrow\) 2(x + y)² \(\ge0\)

\(\Rightarrow\) 2(x + y)² + (y + 1)(1 - x) = 0 \(\Leftrightarrow\) (y + 1)(1 - x) = 0

\(\Rightarrow y+1=0;1-x=0\)

*) y + 1 = 0

y = -1

*) 1 - x = 0

x = 1

Với x = 1; y = -1, ta có:

B = [1 + (-1)]²⁰¹⁸ + (1 - 2)²⁰¹⁸ + (-1 - 1)²⁰¹⁸

= 1 + 2²⁰¹⁸