Đặt 2x^2+2x+1=b;căn(x^2+1)=a>1(do x^2 >=0) 
>>b-2a^2=2x-1>>2b-4a^2=4x-2 
>>2b-4a^2+1=4x-1 
>>(2b-4a^2+1)a=b 
>>b(2a-1)=a(4a^2-1)=a(2a-1)(2a+1) 
>>b=a(2a+1)( Loại 2a-1=0 vì a>1) 
>>b-2a^2 =a>>b-2a^2 =a 
>>2x-1=căn(x^2+1)>>4x^2-4x+1=x^2+1 với x>=1/2 
>>3x^2-4x=0>>x=4/3(Loại x=0 vì x>1/2) 
Vậy x=4/3

Trung  ĐÂU CƠ HỘI CỦA CẬU KÌA    ~~ TÓM LẤY NHANH  VÀ LẸ ĐI

\(\left(t\ge0\right)\)

\(t^2=x+3+6-x+2\sqrt{\left(x+3\right)\left(6-x\right)}\Rightarrow\frac{t^2-9}{2}=\sqrt{\left(x+3\right)\left(6-x\right)}\)

Pt <=> \(t=3+\frac{t^2-9}{2}\)

Bình phương và chuyển vế đc

\(-4\sqrt{ \left(x+3\right)\left(6-x\right)}=\left(x+3\right)\left(6-x\right)\)

Đặt x+3=a

6-x=b

Ta có

\(-4ab=a^2b^2\)

\(a^2b^2+4ab=0\)

<=>ab(ab+4)=0

<=>ab=0 hoặc ab=-4

hỏi j v

a) \(3\sqrt{x}-2\sqrt{9x}+\sqrt{16x}=5\)

\(\Leftrightarrow3\sqrt{x}-6\sqrt{x}+4\sqrt{x}=5\)

\(\Leftrightarrow\sqrt{x}=5\)

<=>  x = 25

b) pt <=> \(\left(x^2+5\right)=\left(x+1\right)^2\)

        <=>  \(\left(x^2+5\right)=x^2+2x+1\)

        <=>   2x = 4

         <=>  x = 2 

c)  pt <=> \(45-14\sqrt{x}+x=x-11\)

         <=> \(45+11=14\sqrt{x}\)

<=> \(56=14\sqrt{x}\)

<=> \(4=\sqrt{x}\)

<=>  x = 16

p/s : Cậu tự đặt điều kiện nhé

\(11\sqrt{5-x}+8\sqrt{2x-1}=24+3\sqrt{\left(5-x\right)\left(2x-1\right)}\)

\(\Leftrightarrow11\sqrt{5-x}+8\sqrt{2x-1}=24+3\sqrt{11x-5-2x^2}\)

\(\Leftrightarrow121\left(5-x\right)+176\sqrt{\left(5-x\right)\left(2x-1\right)}+64\left(2x-1\right)=576+144\sqrt{11x-5-2x^2}\)\(+9\left(11x-5-2x^2\right)\)

\(\Leftrightarrow605-121x+176\sqrt{11x-5-2x^2}+128x-64=576+144\sqrt{11x-5-2x^2}\)\(+99x-18x^2\)

\(\Leftrightarrow176\sqrt{11x-5-2x^2}-144\sqrt{11x-5-2x^2}=531+99x-18x^2-541-7x\)

\(\Leftrightarrow32\sqrt{11x-5-2x^2}=-10+92x-18x^2\)

\(\Leftrightarrow16\sqrt{11x-5-2x^2}=-5+46x-9x^2\)

\(\Leftrightarrow256\left(11x-5-2x^2\right)=25+2116x^2+81x^4-460x+90x^2-823x^3\)

\(\Leftrightarrow2816x-1280-512x^2=25+2206x^2+81x^4-460x-823x^3\)

\(\Leftrightarrow9\left(364x-145-302x^2-9x^4+92x^3\right)=0\)

\(\Leftrightarrow-9x^4+92x^3-302x^2+364x-145=0\)

\(\Leftrightarrow-\left(x-1\right)\left(9x^3-83x^2+219x-145\right)=0\)

\(\Leftrightarrow-\left(x-1\right)\left(x-1\right)\left(9x^2-74x+145\right)=0\)

\(\Leftrightarrow-\left(x-1\right)^2\left(9x-29\right)\left(x-5\right)=0\Leftrightarrow\)x=1; x=29_/9; x=5

\(\Leftrightarrow11\sqrt{5-x}+8\sqrt{2x-1}=24+3\sqrt{11x-5-2x^2}\)