\(-2\left(\sqrt{1+x}+\sqrt{1-x}\right)+7=\sqrt{\left(5-2x\right)\left(5+2x\right)}-2\sqrt{1-x^2}\)

ĐKCĐ: \(-1\le x\le1\)

\(\Leftrightarrow2\left(\sqrt{\left(1-x\right)}-1\right)\left(\sqrt{1+x}-1\right)+5-\sqrt{\left(5-2x\right)\left(5+2x\right)}=0\)

 \(\Leftrightarrow2x^2\left[\frac{2}{5+\sqrt{\left(5-2x\right)\left(5+2x\right)}}-\frac{1}{\left(\sqrt{1-x}+1\right)\left(\sqrt{1+x}+1\right)}\right]\)

Đặt: \(A=\frac{2}{5+\sqrt{\left(5-2x\right)\left(5+2x\right)}}-\frac{1}{\left(\sqrt{1-x}+1\right)\left(\sqrt{1+x}+1\right)}\)

Có: \(A\le\frac{2}{5+\sqrt{\left(5-2\right)\left(5-2\right)}}-\frac{1}{\sqrt{1-x^2}+1+\sqrt{1-x}+\sqrt{1+x}}< \frac{2}{5+3}-\frac{1}{1+1+2}=0\)

\(\Rightarrow x=0\) là nghiệm của pt

x=0. Ai giúp với
 

Mấy ché k giúp ak.

\(\hept{\begin{cases}7\left(2x+y\right)-5\left(3x+y\right)=6\\3\left(x+2y\right)-2\left(x+3y\right)=-6\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}14x+7y-15x-5y=6\\3x+6y-2x-6y=-6\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}-x+2y=6\\x=-6\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=-6\\y=0\end{cases}}\)

\(x^5+y^5-\left(x+y\right)^5\)

\(=x^5+y^5-\left(x^5+5x^4y+10x^3y^2+10x^2y^3+8xy^4+y^5\right)\)

\(=-5xy\left(x^3+2x^2y+2xy^2+y^3\right)\)

\(=-5xy\left[\left(x+y\right)\left(x^2-xy+y^2\right)+2xy\left(x+y\right)\right]\)

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

a)\(\left(x-2\right)\left(5-x\right)=7x-\left(x-1\right)\left(3-2x\right)\Leftrightarrow5x-x^2-10+2x=7x-3x+2x^2+3-2x\Leftrightarrow-3x^2+5x-13=0\)\(\Delta=b^2-4ac=25-4.\left(-3\right).\left(-13\right)=-131< 0\)

\(\Rightarrow\)phương trình vô nghiệm

Dùng liên hợp.

pt <=> \(\left(x-\sqrt{2}\right)\left(x-\sqrt{3}\right)\left(1+\sqrt{2}\right)\left(1+\sqrt{3}\right)\)

\(-3\left(x-1\right)\left(x-\sqrt{3}\right)\left(\sqrt{2}+1\right)\left(\sqrt{2}+\sqrt{3}\right)\)

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

<=> \(\left(x-\sqrt{3}\right)\left(1+\sqrt{2}\right)\left[\left(x-\sqrt{2}\right)\left(1+\sqrt{3}\right)-\left(x-1\right)\left(\sqrt{2}+\sqrt{3}\right)\right]\)

\(-2\left(x-1\right)\left(\sqrt{3}+\sqrt{2}\right)\left[\left(x-\sqrt{3}\right)\left(1+\sqrt{2}\right)-\left(x-\sqrt{2}\right)\left(1+\sqrt{3}\right)\right]\)

\(=3x-1\)

<=> \(\left(x-\sqrt{3}\right)\left(1+\sqrt{2}\right)\left(x+\sqrt{3}\right)\left(1-\sqrt{2}\right)\)

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

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

<=> \(x^2-3x+2=0\) phương trình bậc 2.

Em làm tiếp nhé!

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

\(\Leftrightarrow6x-2-5-3x=6x-3\)

\(\Leftrightarrow6x-3x-6x=-3+2+5\)

\(\Leftrightarrow-3x=4\)

\(\Leftrightarrow x=-\frac{4}{3}\)

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

\(\Leftrightarrow3x-\frac{3}{2}+\frac{4}{3}x-\frac{4}{3}=\frac{x}{4}\)

\(\Leftrightarrow3x+\frac{4}{3}x-\frac{x}{4}=\frac{3}{2}+\frac{4}{3}\)

\(\Leftrightarrow\frac{49}{12}x=\frac{17}{6}\)

\(\Leftrightarrow x=\frac{34}{49}\)

c) \(\frac{1}{5}\left(x-\frac{1}{3}\right)-4\left(\frac{x}{5}-\frac{1}{2}\right)=x\)

\(\Leftrightarrow\frac{1}{5}x-\frac{1}{15}-\frac{4}{5}x+2=x\)

\(\Leftrightarrow\frac{1}{5}x-\frac{4}{5}x-x=\frac{1}{15}-2\)

\(\Leftrightarrow-\frac{8}{5}x=-\frac{29}{15}\)

\(\Leftrightarrow x=\frac{29}{24}\)

Câu hỏi của Phương Boice - Toán lớp 8 - Học toán với OnlineMath

Đặt \(\sqrt{x^2-x+1}=a\left(ĐK:a>0\right)\)

\(pt\Leftrightarrow\frac{\left(x^6+3x^4a\right)\left(4-a^2\right)}{4\left(2+a\right)a^2}=a\left(2-a\right)\)

\(\Leftrightarrow\left(x^6+3x^4a\right)\left(4-a^2\right)=4a^3\left(4-a^2\right)\)

\(\Leftrightarrow\left(4-a^2\right)\left(x^6+3x^4a-4a^3\right)=0\)

TH1: \(4-a^2=0\Leftrightarrow\orbr{\begin{cases}a=-2\left(l\right)\\a=2\left(n\right)\end{cases}}\)

Với a = 2 , \(\sqrt{x^2-x+1}=2\Rightarrow x^2-x-3=0\Rightarrow\orbr{\begin{cases}x=\frac{\sqrt{13}+1}{2}\\x=\frac{-\sqrt{13}+1}{2}\end{cases}}\)

TH2: \(x^6+3x^4a-4a^3=0\Rightarrow x^6-x^4a+4x^4a-4x^2a^2+4x^2a^2-4a^3=0\)

\(\Leftrightarrow\left(x^2-a\right)\left(x^4+4x^2a+4a^2\right)=0\Leftrightarrow\left(x^2-a\right)\left(x^2+2a\right)^2=0\)

\(\Leftrightarrow\orbr{\begin{cases}x^2=a\\x^2=-2a\left(l\right)\end{cases}}\)

Với \(x^2=a\Rightarrow x^2=\sqrt{x^2-x+1}\)

Đến đây bình phương và tìm ra nghiệm.

Khó ghê, có quản lí mới giải được

KHÓ thật đấy có quản lí mới giải được thôi