Đặt \(a=\sqrt[3]{3x+1};b=\sqrt[3]{3x-1}\)=>a3 -b3 =2
pt ,<=> a2 +b2 +ab =1 (1)
Mà a3 - b3 = ( a-b)(a2+b2+ab) =2
=> a -b =2 (*)
=> a2 +b2 -2ab =4 (2)
(1)(2)=> 3ab =-3 => ab =-1 => a(-b) =1 (**)
(*)(**)=> a ; -b là nghiệm của pt: x2 -2x+1=0 => a =-b =1
=> \(3x+1=1\Rightarrow x=0\)
và \(3x-1=-1\Rightarrow x=0\)
Vây x =0 (TM)
Giải pt sau
\(\sqrt[3]{\left(3x+1\right)^2}+\sqrt[3]{\left(3x-1\right)^2}+\sqrt[3]{9x^2-1}=1\)
giải pt
\(\frac{2\left(x-\sqrt{2}\right)\left(x-\sqrt{3}\right)}{\left(1-\sqrt{2}\right)\left(1-\sqrt{3}\right)}+\frac{3\left(x-1\right)\left(x-\sqrt{3}\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}-\sqrt{3}\right)}+\frac{4\left(x-1\right)\left(x-\sqrt{2}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-2\right)}\)=3x-1
Áp dụng nội suy niu tơn để giải pt sau
\(\frac{2\left(x-\sqrt{2}\right)\left(x-\sqrt{3}\right)}{\left(1-\sqrt{2}\right)\left(1-\sqrt{3}\right)}+\frac{3\left(x-1\right)\left(x-\sqrt{3}\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}-\sqrt{3}\right)}+\frac{4\left(x-1\right)\left(x-\sqrt{2}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-\sqrt{2}\right)}=3x-1\)
Ai dậy r giúp vs :33 1 câu cx đc nhé :v toàn giải pt hết nhé
1) \(4x^2+\left(8x-4\right)\sqrt{x}-1=3x+2\sqrt{2x^2+5x-3}.\)
2) \(\left(5x+8\right)\sqrt{2x-1}+7x\sqrt{x+3}=9x+18-\left(x+26\right)\sqrt{x-1}\)
3) \(\sqrt[3]{3x+1}+\sqrt[3]{5-x}+\sqrt[3]{2x-9}-\sqrt[3]{4x-3}=0\)
4) \(\left(x+17\right)\sqrt{4-x}+\left(20-x\right)\sqrt{x+1}-9\sqrt{4-x}.\sqrt{x+1}=36\)
giải pt: \(\sqrt{3x^2-5x+1}-\sqrt{x^2-2}=\sqrt{3\left(x^2-x-1\right)}-\sqrt{x^2-3x+4}\)
Giải các phương trình :
a) \(3x^2-6x-4=4\left(x-1\right)\sqrt{3x+1}\)
b) \(\sqrt{6x-1}+\sqrt{9x^2-1}=6x-9x^2\)
c) \(3\left(\sqrt{2x-1}+\sqrt{x+3}\right)-2\sqrt{2x^2+5x-3}=3x+4\)
Giải PT
\(\sqrt{4x-20}-3\sqrt{\frac{x-5}{9}}=\sqrt{1-x}\)
\(\sqrt{4x+8}+2\sqrt{x+2}-\sqrt{9x+18}=1\)
\(\sqrt{3x^2-4x+3}=1-2x\)
\(\sqrt{16\left(x+1\right)}-\sqrt{9\left(x+1\right)}=4\)
Giải PT sau: \(\sqrt{3x^2}\) \(-\) \(\left(1-\sqrt{3}\right)\)x \(-\) 1 = 0
giải phương trình
\(\left(2x+1\right)\left(2+\sqrt{4x^2+4x+1}\right)+3x\left(2x+\sqrt{9x^2+3}\right)=0\)