GPT
\(a,\left(x^2-5x+1\right)\left(x^2-4\right)=6\left(x-1\right)^2\)
NQ
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GPT
\($x^4+\left(x+1\right)\left(5x^2-6x-6\right)=0$\)
GPT: \(\log_2\left(\sqrt{x^2-5x+5}+1\right)+\log_3\left(x^2-5x+7\right)=2\)
Đặt \(\sqrt{x^2-5x+5}=t>0\)
\(\Rightarrow log_2\left(t+1\right)+log_3\left(t^2+2\right)-2=0\)
Nhận thấy \(t=1\) là 1 nghiệm của pt
Xét hàm \(f\left(t\right)=log_2\left(t+1\right)+log_3\left(t^2+2\right)-2\)
\(f'\left(t\right)=\dfrac{1}{\left(t+1\right)ln2}+\dfrac{2t}{\left(t^2+2\right)ln3}>0\Rightarrow f\left(t\right)\) đồng biến
\(\Rightarrow f\left(t\right)\) có tối đa 1 nghiệm
\(\Rightarrow t=1\) là nghiệm duy nhất của pt
\(\Rightarrow\sqrt{x^2-5x+5}=1\Rightarrow\left[{}\begin{matrix}x=1\\x=4\end{matrix}\right.\)
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gpt:
\(3\left(x^2-3x+1\right)+\sqrt{3\left(x^4+x^2+1\right)}=0\)
\(\sqrt[3]{x^3+5x^2}-1=\sqrt{\frac{5x^2-2}{6}}\)
Gpt:
a.\(\left(x^2-4x+3\right)^3+\left(x^2-7x+6\right)^3=\left(2x^2-11x+9\right)^3\)
b.\(\left(x+1\right)\left(x-4\right)\left(x+2\right)\left(x-8\right)+4x^2=0\)
a)Dat \(x^2-4x+3=a;x^2-7x+6=b \Rightarrow a+b=2x^2-11x+9\)
....
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\(gpt\\ 8\left(x+\dfrac{1}{x}\right)^2+4\left(x^2+\dfrac{1}{x^2}\right)^2-4\left(x^2+\dfrac{1}{x^2}\right)\left(x+\dfrac{1}{x}\right)^2=\left(x+4\right)^2\)
ĐKXĐ:x khác 0
Xét VT=\(8\left(x+\dfrac{1}{x}\right)^2+4\left(x^2+\dfrac{1}{x^2}\right)-4\left(x^2+\dfrac{1}{x^2}\right)\left(x+\dfrac{1}{x}\right)^2=8\left(x+\dfrac{1}{x}\right)^2+4\left(x^2+\dfrac{1}{x^2}\right)^2-4\left(x^2+\dfrac{1}{x^2}\right)\left(x^2+\dfrac{1}{x^2}+2\right)=8\left(x+\dfrac{1}{x}\right)^2+4\left(x^2+\dfrac{1}{x^2}\right)^2-4\left(x^2+\dfrac{1}{x^2}\right)^2-8\left(x^2+\dfrac{1}{x^2}\right)=8\left(x^2+\dfrac{1}{x^2}+2\right)-8\left(x^2+\dfrac{1}{x^2}\right)=16\)
=>(x+4)2=16
<=>x+4=4 hoặc x+4=-4
<=>x=0(L) hoặc x=-8(TM)
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giải phương trình
\(-6\left(-x^2-x+1\right)^4+x^2\left(-x^2-x+1\right)^2+5x^4=0\)
b) \(x^4+9=5x\left(x^2-3\right)\)
c) \(x^4+\left(x+1\right)\left(5x^2-6x-6\right)=0\)
d)\(\left(x^2+1\right)^2+\left(x+1\right)\left(3x^2+2x-2\right)=0\)
e) \(x^2\left(x-1\right)^2+x\left(x^2-1\right)=2\left(x+1\right)^2\)
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GPT:
\(\left(1\right)\left(2-3x\right)\left(x+11\right)=\left(3x-2\right)\left(2-5x\right)\)
\(\left(2\right)\frac{x-3}{x+3}-\frac{x+3}{x-3}=-\frac{5}{x^2-9}\)
\(\left(1\right)\Leftrightarrow2x-3x^2+11-33x=6x-4-15x^2+10x\)
\(\Leftrightarrow12x^2-47x+15=0\)
\(\Delta=47^2-4.12.15=1489,\sqrt{\Delta}=\sqrt{1489}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{47+\sqrt{1489}}{24}\\x=\frac{47-\sqrt{1489}}{24}\end{cases}}\)
\(\left(2\right)\Leftrightarrow\frac{\left(x-3\right)^2-\left(x+3\right)^2}{x^2-9}=\frac{-5}{x^2-9}\)
\(\Leftrightarrow\left(x-3\right)^2-\left(x+3\right)^2=-5\)
\(\Leftrightarrow x^2-6x+9-x^2-6x-9=-5\)
\(\Leftrightarrow-12x=-5\Leftrightarrow x=\frac{5}{12}\)
(2-3x)(x+11)=(3x-2)(2-5x)
<=>(3x-2)(2-5x)-(2-3x)(x+11)=0
<=>(3x-2)(2-5x)+(3x-2)(x+11)=0
<=>(3x-2)[2-5x+x+11]=0
<=>(3x-2)(13-4x)=0
<=>\(\orbr{\begin{cases}3x-2=0\\13-4x=0\end{cases}}\)
<=>\(\orbr{\begin{cases}x=\frac{2}{3}\\x=\frac{13}{4}\end{cases}}\)
\(\frac{x-3}{x+3}-\frac{x+3}{x-3}=-\frac{5}{x^2-9}\)
Đk:\(x\ne-3;x\ne3\)(*)
Với đk trên pt tương đương với:
\(\frac{\left(x-3\right)^2-\left(x+3\right)^2}{\left(x+3\right)\left(x-3\right)}=-\frac{5}{\left(x+3\right)\left(x-3\right)}\)
\(x^2-6x+9-x^2-6x-9=-5.-12x=-5\)
\(x=\frac{15}{12}\left(tmđk\right)\)(*)
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GPT:\(\frac{\left(x+1\right)\left(x+28\right)\left(x+4\right)\left(x-10\right)\left(-5\right)}{\sqrt{x}\left(x-6\right)^{\frac{1}{2}}}\ln\left(x^2-10\right)=0\)
Nhân tài đâu giúp mình với mình tick cho
Tìm x biết : (đề không sai)
1.-4xleft(x-7right)+4xleft(x^2-5right) 28x^2-13
2.left(4x^2-5xright)left(3x+2right)-7xleft(x-7right) left(-4+xright)left(-2x+3right)+12x^3+2x^2
3.left(-4x^2-3right)left(2x+5right)-left(8x-3right) left(-x^2+2right)-5x^2left(x-6right)-3x^2-4
4.left(x-7right)left(x+5right)-left(x-3right)left(x-2right) 15x^2left(x+1right)-left(3x^2-1right) left(5x^2-2right)-21x^2
5.left(x-3right)left(-x+10right)+left(x-8right)left(x+3right) left(5x^2-1right)left(x+3right)-5x^3-15x^2...
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Tìm x biết : (đề không sai)
1.\(-4x\left(x-7\right)+4x\left(x^2-5\right)\) \(=28x^2-13\)
2.\(\left(4x^2-5x\right)\left(3x+2\right)-7x\left(x-7\right)\)= \(\left(-4+x\right)\left(-2x+3\right)+12x^3+2x^2\)
3.\(\left(-4x^2-3\right)\left(2x+5\right)-\left(8x-3\right)\) \(\left(-x^2+2\right)=-5x^2\left(x-6\right)-3x^2-4\)
4.\(\left(x-7\right)\left(x+5\right)-\left(x-3\right)\left(x-2\right)\) \(=15x^2\left(x+1\right)-\left(3x^2-1\right)\) \(\left(5x^2-2\right)-21x^2\)
5.\(\left(x-3\right)\left(-x+10\right)+\left(x-8\right)\left(x+3\right)\) \(=\left(5x^2-1\right)\left(x+3\right)-5x^3-15x^2\)
6.\(\left(-2x^2+5\right)\left(-x+3\right)-x^2\left(2x-6\right)\) \(=\left(x-1\right)\left(x+1\right)-\left(x-2\right)\left(x+4\right)\)