Giai pt : \(x+\frac{2a\left(x+a\right)}{x}=\frac{a^2}{x}.\)
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Gỉai pt : \(x+\frac{2a\left|x+a\right|}{x}=\frac{a^2}{x}\)
Phương trình đã cho tương đương với \(x^2+2a\left|x+a\right|-a^2=0\) với \(x\ne0\)
\(\left|x+a\right|=\begin{cases}x+a\left(x\ge-a\right)\\-\left(x+a\right)\left(x< -a\right)\end{cases}\)
TH1 : Với \(x< -a:x^2-2a\left(x+a\right)-a^2=0\) với \(x\ne0\)
\(\Leftrightarrow x^2-2ax-3a^2=0\)
\(\Leftrightarrow\left(x+a\right)\left(x-3a\right)=0\) với \(x\ne0\)
\(x=3a< -a\Leftrightarrow x=3a\) với \(a< 0\).
TH2 : Với \(x\ge-a:x^2+2a\left(x+a\right)-a^2=0\) với \(x\ne0\) \(\Leftrightarrow x^2+2ax+a^2=0\)
\(\Leftrightarrow\left(x+a\right)^2=0\Leftrightarrow x=-a.\)Tóm lại : \(a=0:\)Vô nghiệm
\(a>0:\)một nghiệm \(x=-a\) ; \(a< 0\) : hai nghiệm \(x_1=-4;x_2=3a.\)
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Giai pt sau:
\(\frac{\left(b-c\right)\left(1+a\right)^2}{x+a^2}+\frac{\left(c-a\right)\left(1+b\right)^2}{x+b^2}+\frac{\left(a-b\right)\left(1+c\right)^2}{x+c^2}=0\)
Cho :\(A=\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{x+3};B=\frac{a}{x\left(x+a\right)}+\frac{a}{\left(x+a\right)\left(x+2a\right)}+\frac{a}{\left(x+2a\right)\left(x+3a\right)}+\frac{1}{x+3a}\)CMR : A = B
giai pt:\(\frac{\left|x-3\right|}{4}-\frac{\left|x-4\right|}{9}=\frac{1}{2}-\frac{x+5}{36}.\)
GIAI PT: \(\frac{3}{\left(X-1\right)\left(X-2\right)}\)-\(\frac{2}{\left(X-3\right)\left(X-1\right)}\)=\(\frac{1}{\left(X-2\right)\left(X-3\right)}\) tim dkxd
ĐKXĐ: \(\left\{{}\begin{matrix}x-1\ne0\\x-2\ne0\\x-3\ne0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\ne1\\x\ne2\\x\ne3\end{matrix}\right.\)
\(\frac{3}{\left(x-1\right)\left(x-2\right)}-\frac{2}{\left(x-3\right)\left(x-1\right)}=\frac{1}{\left(x-2\right)\left(x-3\right)}\)
\(\frac{3\left(x-3\right)}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}-\frac{2\left(x-2\right)}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}-\frac{x-1}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}=0\)
\(3x-9-2x+4-x+1=0\)
\(0x-4=0\Rightarrow0x=4\Rightarrow\) Phương trình vô nghiệm
a) Tìm m để pt \(\left(x^2-1\right)\left(x+3\right)\left(x+5\right)=m\) có 4 nghiệm thỏa: \(\frac{1}{x_1}+\frac{1}{x_2}+\frac{1}{x_3}+\frac{1}{x_4}=-1\)
b) Tìm các số \(a,b,c\ge0\)sao cho: \(\left(a^2+b+\frac{3}{4}\right)\left(b^2+a+\frac{3}{4}\right)=\left(2a+\frac{1}{2}\right)\left(2b+\frac{1}{2}\right)\)
1. Cho pt: x2 -2(m+1)x+m20 (1). Tìm m để pt có 2 nghiệm x1 ; x2 thỏa mãn (x1-m)2 + x2m+2.
2. Giai pt: left(x-1right)sqrt{2left(x^2+4right)}x^2-x-2
3. Giai hệ pt: left{{}begin{matrix}frac{1}{sqrt[]{x}}-frac{sqrt{x}}{y}x^2+xy-2y^2left(1right)left(sqrt{x+3}-sqrt{y}right)left(1+sqrt{x^2+3x}right)3left(2right)end{matrix}right.
4. Giai pt trên tập số nguyên x^{2015}sqrt{yleft(y+1right)left(y+2right)left(y+3right)}+1
Đọc tiếp
1. Cho pt: x2 -2(m+1)x+m2=0 (1). Tìm m để pt có 2 nghiệm x1 ; x2 thỏa mãn (x1-m)2 + x2=m+2.
2. Giai pt: \(\left(x-1\right)\sqrt{2\left(x^2+4\right)}=x^2-x-2\)
3. Giai hệ pt: \(\left\{{}\begin{matrix}\frac{1}{\sqrt[]{x}}-\frac{\sqrt{x}}{y}=x^2+xy-2y^2\left(1\right)\\\left(\sqrt{x+3}-\sqrt{y}\right)\left(1+\sqrt{x^2+3x}\right)=3\left(2\right)\end{matrix}\right.\)
4. Giai pt trên tập số nguyên \(x^{2015}=\sqrt{y\left(y+1\right)\left(y+2\right)\left(y+3\right)}+1\)
Gọi a là nghiệm của pt: \(\sqrt{2}x^2+x-1=0\). Không giải pt,tính:
\(A=\frac{2a-3}{\sqrt{2\left(2a^4-2a+3\right)}+2a^2}\)
2a^4=(1-a)^2=a^2-2a+1
\(A=\frac{2a-3}{\sqrt{2\left(a^2-4a+4\right)}+2a^2}=\frac{2a-3}{\sqrt{2}!\left(a-2\right)!+2a^2}\)a> 2 không thể là nghiệm=> a<2
\(A=\frac{2a-3}{\sqrt{2}\left(2-a\right)+2a^2}=\frac{2a-3}{2a^2-\sqrt{2}a+2\sqrt{2}}=\frac{2a-3}{\sqrt{2}\left(\sqrt{2}a^2-a-1+3\right)}\)
\(A=\frac{2a-3}{\sqrt{2}\left(3\right)}\)
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a là nghiệm =>\(\sqrt{2}a^2+a-1=0\Rightarrow\sqrt{2}a^2=1-a\\\)\(2a^4=\left(1-a\right)^2=1^2-2a+a^2\)
Thay 2a^4=...vào ==>
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Xem thêm câu trả lời
Giải các pt sau:
a)2(x-1)x-a(x-1)=2a+3
b)\(\frac{x+1}{2}\)+\(\frac{x+2}{3}\)+\(\frac{x+3}{4}\)=3
c)\(\frac{3x}{x-2}\)+\(\frac{-x}{x-5}\)+\(\frac{3x}{\left(x-2\right)\left(x-5\right)}\)=0
a) \(2\left(x-1\right)-a\left(x-1\right)=2a+3\)
\(\Leftrightarrow2a-2-ax+a=2a+3\)
\(\Leftrightarrow-2-ax+a=3\)
\(\Leftrightarrow-a\left(x-1\right)=5\)
\(\Leftrightarrow\left(x-1\right)=\frac{-5}{a}\Leftrightarrow x=\frac{a-5}{a}\)
b) \(\frac{x+1}{2}+\frac{x+2}{3}+\frac{x+3}{4}=3\)
\(\Leftrightarrow\frac{12x+12+8x+16+6x+18}{24}=3\)
\(\Leftrightarrow12x+12+8x+16+6x+18=72\)
\(\Leftrightarrow26x+46=72\)
\(\Leftrightarrow26x=26\Leftrightarrow x=1\)
c) \(ĐKXĐ:x\ne2;x\ne5\)
\(\frac{3x}{x-2}+\frac{-x}{x-5}+\frac{3x}{\left(x-2\right)\left(x-5\right)}=0\)
\(\Rightarrow\frac{3x\left(x-5\right)-x\left(x-2\right)+3x}{\left(x-2\right)\left(x-5\right)}=0\)
\(\Rightarrow3x\left(x-5\right)-x\left(x-2\right)+3x=0\)
\(\Rightarrow3x^2-15x-x^2+2x+3x=0\)
\(\Leftrightarrow2x^2-10x=0\)
\(\Leftrightarrow2x\left(x-5\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x=5\end{cases}}\)