Ta có x = 12√√2−1√2+1122−12+1 = √2−122−12
⇒2x=√2−1⇒2x=2−1.
Mà có 4x2+4x-1 = (√2−1)2+2(√2−1)−1=0(2−1)2+2(2−1)−1=0
Mặt khác 4x5 + 4x4-5x3 + 5x- 2= x3 (4x2+4x-1) -x (4x2+ 4x -1) +(4x2 +4x-1) -1
= (x3-x+1)(4x2+4x-1) -1 =-1
a)\(\sqrt{1-x}\left(x-3x^2\right)=x^3-3x^2+2x+6\)
b)\(x^2+x+12\sqrt{x+1}=36\)
c)\(3x-1+\frac{x-1}{4x}=\sqrt{3x+1}\)
d)\(\sqrt{x^2+12}-3x=\sqrt{x^2+5}-5\)
e)\(4x^2+12+\sqrt{x-1}=4\left(x\sqrt{5x-1}+\sqrt{9-5x}\right)\)
f)\(4x^3-25x^2+43x+x\sqrt{3x-2}=22+\sqrt{3x-2}\)
g)\(2\left(x+1\right)\sqrt{x}+\sqrt{3\left(2x^3+5x^2+4x+1\right)}=5x^3-3x^2+8\)
h)\(\sqrt{x^2+12}-\sqrt{x^2+5}=3x-5\)
i)\(\sqrt{1-3x}-\sqrt[3]{3x-1}=\left|6x-2\right|\)
k)\(\sqrt{2x^3+3x^2-1}=2x^2+2x-x^3-1\)
l)\(\sqrt{x^2+x-2}+x^2=\sqrt{2\left(x-1\right)}+1\)
Giải các pt sau:
a) \(\sqrt{x+8}+\frac{9x}{\sqrt{x+8}}-6\sqrt{x}=0\)
b) \(x^4-2x^3+\sqrt{2x^3+x^2+2}-2=0\)
c) \(3x\sqrt[3]{x+7}\left(x+\sqrt[3]{x+7}\right)=7x^3+12x^2+5x-6\)
d) \(4x^2+\left(8x-4\right)\sqrt{x}-1=3x+2\sqrt{2x^2+5x-3}\)
e) \(16x^2+19x+7+4\sqrt{-3x^2+5x+2}=\left(8x+2\right)\left(\sqrt{2-x}+2\sqrt{3x+1}\right)\)
f) \(\left(5x+8\right)\sqrt{2x-1}+7x\sqrt{x+3}=9x+8-\left(x+26\right)\sqrt{x-1}\)
g) \(\sqrt[3]{3x+1}+\sqrt[3]{5-x}+\sqrt[3]{2x-9}-\sqrt[3]{4x-3}=0\)
Cho x=\(\dfrac{1}{2}\sqrt{\dfrac{\sqrt{2}-1}{\sqrt{2}+1}}\). Tính A=(4x5+4x4-x3+1)19+\(\sqrt{4x^5+4x^4-5x^3+5x}\)+\(\left(\dfrac{1-\sqrt{2}x}{\sqrt{2x^2+2x}}\right)^{2019}\)
1) giải hệ phương trình \(\left\{{}\begin{matrix}\left(2x+4y-1\right)\sqrt{2x-y-1}=\left(4x-2y-3\right)\sqrt{x+2y}\left(1\right)\\x^2+8x+5-2\left(3y+2\right)\sqrt{4x-3y}=2\sqrt{2x^2+5x+2}\left(2\right)\end{matrix}\right.\)
2) cho a,b,c là các số thực dương thỏa mãn ab+2bc+2ca=7. tim GTNN của biểu thức \(Q=\frac{11a+11b+12c}{\sqrt{8a^2+56}+\sqrt{8b^2+56}+\sqrt{4c^2+7}}\)
\(A=\left(4x^5+4x^4-5x^3+5x-2\right)^{2017}+2019.\) với \(x=\dfrac{1}{2}\sqrt{\dfrac{\sqrt{2}-1}{\sqrt{2}+1}}\)
Giải phương trình:
1, \(4\left(2x^2+1\right)+3\left(x^2-2x\right)\sqrt{2x-1}=2\left(x^3+5x\right)\)
2, \(\sqrt{5x^2+4x}-\sqrt{x^2-3x-18}=5\sqrt{x}\)
3, \(\sqrt{5x^2-14x+9}-\sqrt{x^2-x-20}=5\sqrt{x+1}\)
1. giải pt và hpt : a) \(3x-16y-24=\sqrt{9x^2+16x+32}\) (\(x,y\in N\)*)
b) \(4x^3+5x^2+1=\sqrt{3x+1}-3x\)
c) \(\left\{{}\begin{matrix}y^2\sqrt{2x-1}+\sqrt{3}=5y^2-\sqrt{6x-3}\\2y^4\left(5x^2-17x+6\right)=6-15x\end{matrix}\right.\)
2. \(\left\{{}\begin{matrix}a,b,c\ge1\\32abc=18\left(a+b+c\right)+24\end{matrix}\right.\) Tìm Max \(P=\frac{\sqrt{a^2-1}}{a}+\frac{\sqrt{b^2-1}}{b}+\frac{\sqrt{c^2-1}}{c}\)
giải phương trình ( đặt ẩn phụ )
1)\(\sqrt{2x+\sqrt{4x^2-1}}\)+\(\sqrt{2x-\sqrt{4x^2-1}}\)=2
2)(x+5)(2-x)=3.\(\sqrt{x^3+3x}\)
3) 4x2 +10x+9=5. \(\sqrt{2x^2+5x+3}\)
4) \(\frac{x}{x+1}-2\sqrt{\frac{x+1}{2}}\)=3
5)\(\sqrt{x+1}\)+\(\sqrt{4-x}\)+\(\sqrt{\left(x+1\right)\left(4-x\right)}\)=5
6) \(\sqrt{2-x}\)+\(\sqrt{x+2}\)+\(\sqrt{4-x^2}\)=2
Giải pt : a) \(8x^2-13x+7=\left(1+\frac{1}{x}\right)\sqrt[3]{3x^2-2}\)
b) \(\sqrt{4x^2+5x+1}-2\sqrt{x^2-x+1}=9x-3\)
c) \(2\sqrt{x+1}+6\sqrt{9-x^2}+6\sqrt{\left(x+1\right)\left(9-x^2\right)}=38+10x-2x^2-x^3\)
