\(\sqrt{2x-3}+\sqrt{5-2x}=3x^2-12x+14\) \(\left(\dfrac{3}{2}\text{≤}x\text{≤}\dfrac{5}{2}\right)\)
\(\text{⇔}2\sqrt{2x-3}+2\sqrt{5-2x}=6x^2-24x+28\)
\(\text{⇔}2x-3-2\sqrt{2x-3}+1+5-2x-2\sqrt{5-2x}+1+6x^2-24x+24=0\) \(\text{⇔}\left(\sqrt{2x-3}-1\right)^2+\left(\sqrt{5-2x}-1\right)^2+6\left(x-2\right)^2=0\)
\(\text{⇔}x=2\left(TM\right)\)
KL.............
Giải phương trình:
\(\sqrt{2x-3}+\sqrt{5-2x}=3x^2-12x+14\)
Giải các pt sau:
1, \(\sqrt{x^2+x+1}=2x+\sqrt{x^2-x+1}\)
2, \(2x^2+2x+6=2x\sqrt{x^2-x+1}+4\sqrt{3x+1}\)
3, \(\left(\sqrt{x+3}-\sqrt{x}\right)\left(1+\sqrt{x^2+3x}\right)=3\)
4, \(\sqrt{2x^2-1}+\sqrt{x^2-3x-2}=\sqrt{2x^2-2x+3}+\sqrt{x^2-x+2}\)
5, \(13\sqrt{x-1}+9\sqrt{x+1}=16x\)
Giải pt \(x\left(3-\sqrt{3x-1}\right)=\sqrt{3x^2+2x-1}-x\sqrt{x+1}+1\)
Giải pt:
\(a)x^{4}-2\sqrt{2}x^{2}+2=\sqrt{2}+x \\b)(2x+3)\sqrt{x^{2}-2}=2x^{2}+3x-4 \\c)2x^{2}+2(x+1)\sqrt{x^{2}-1}-6x+1=0\)
giải pt vô tỉ sau bằng phương pháp đặt ẩn phụ
a)\(3\left(\sqrt{2x^2+1}-1\right)=x\left(1+3x+8\sqrt{2x^2+1}\right)\)
b)\(\sqrt[3]{x+5}+\sqrt[3]{4-x}=\sqrt[3]{x+24}\)
Giải pt:
\(4\sqrt{x^2+3x}+2\sqrt{2x-1}=7x+3\)
Giải các pt sau:\(\sqrt{x^2-2x+1}+\sqrt{x^2-4x+4}=3\)
\(\sqrt{x^2-10x+25}=3-19x\)
\(\sqrt{2x-2+2\sqrt{2x-3}}+\sqrt{2x+13+8\sqrt{2x-3}}=5\)
Giải PT:
a) \(\dfrac{9x-7}{\sqrt{7x+5}}=\sqrt{7x+5}.\)
b) \(\sqrt{4x-20}+3\sqrt{\dfrac{x-5}{9}}-\dfrac{1}{3}\sqrt{9x-45}=4.\)
c) \(2x-x^2+\sqrt{6x^2-12x+7}=0.\)
d) \(\left(x+1\right)\left(x+4\right)-3\sqrt{x^2+5x+2}=6.\)
Giải PT: \(2x+3=2\sqrt{x+1}+\sqrt{2x+1}\)