1) \(x^4-6x^3-x^2+54x-72=0\)

\(\Leftrightarrow x^3\left(x-2\right)-4x^2\left(x-2\right)-9x\left(x-2\right)+36\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x^3-4x^2-9x+36\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left[x^2\left(x-4\right)-9\left(x-4\right)\right]=0\)

\(\Leftrightarrow\left(x-2\right)\left(x-4\right)\left(x^2-9\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x-4\right)\left(x-3\right)\left(x+3\right)=0\)

Tự làm nốt...

2) \(x^4-5x^2+4=0\)

\(\Leftrightarrow x^2\left(x^2-1\right)-4\left(x^2-1\right)=0\)

\(\Leftrightarrow\left(x^2-1\right)\left(x^2-4\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)=0\)

Tự làm nốt...

\(x^4-2x^3-6x^2+8x+8=0\)

\(\Leftrightarrow x^3\left(x-2\right)-6x\left(x-2\right)-4\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x^3-6x-4\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left[x^2\left(x+2\right)-2x\left(x+2\right)-2\left(x+2\right)\right]=0\)

\(\Leftrightarrow\left(x-2\right)\left(x+2\right)\left(x^2-2x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x+2\right)\left[\left(x-1\right)^2-\left(\sqrt{3}\right)^2\right]=0\)

\(\Leftrightarrow\left(x-2\right)\left(x+2\right)\left(x-1-\sqrt{3}\right)\left(x-1+\sqrt{3}\right)=0\)

...

\(2x^4-13x^3+20x^2-3x-2=0\)

\(\Leftrightarrow2x^3\left(x-2\right)-9x^2\left(x-2\right)+2x\left(x-2\right)+\left(x-2\right)=0\)

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

Bí

\(2x^3-9x^2+2x+1\)

\(=2x^3-x^2-8x^2+4x-2x+1\)

\(=x^2\left(2x-1\right)-4x\left(2x-1\right)-\left(2x-1\right)\)

\(=\left(2x-1\right)\left(x^2-4x-1\right)\)

\(=\left(2x-1\right)\left(x^2-4x+4-5\right)\)

\(=\left(2x-1\right)\left[\left(x-2\right)^2-5\right]\)

.......

ĐKXĐ: \(x\ge0\)

\(\sqrt{2x^2+8x+5}-4\sqrt{x}+\sqrt{2x^2-4x+5}-2\sqrt{x}=0\)

\(\Leftrightarrow\dfrac{2x^2-8x+5}{\sqrt{2x^2+8x+5}+4\sqrt{x}}+\dfrac{2x^2-8x+5}{\sqrt{2x^2-4x+5}+2\sqrt{x}}=0\)

\(\Leftrightarrow\left(2x^2-8x+5\right)\left(\dfrac{1}{\sqrt{2x^2+8x+5}+4\sqrt{x}}+\dfrac{1}{\sqrt{2x^2-4x+5}+2\sqrt{x}}\right)=0\)

\(\Leftrightarrow2x^2-8x+5=0\)

\(\Leftrightarrow...\)

a)\(\sqrt{2x^2+8x+6}+\sqrt{x^2-1}=2x+2\)

ĐK:tự xác định 

\(pt\Leftrightarrow\sqrt{2\left(x+1\right)\left(x+3\right)}+\sqrt{\left(x-1\right)\left(x+1\right)}-2\left(x+1\right)=0\)

\(\Leftrightarrow\sqrt{x+1}\left(\sqrt{2\left(x+3\right)}+\sqrt{x-1}-2\sqrt{x+1}\right)=0\)

Suy ra x=-1 là nghiệm và pt \(\sqrt{2\left(x+3\right)}+\sqrt{x-1}=2\sqrt{x+1}\)

\(\Leftrightarrow2\left(x+3\right)+x-1+2\sqrt{2\left(x+3\right)\left(x-1\right)}=4\left(x+1\right)\)

\(\Leftrightarrow2\sqrt{2\left(x+3\right)\left(x-1\right)}=x-1\)

\(\Leftrightarrow8\left(x+3\right)\left(x-1\right)-\left(x-1\right)^2=0\)

\(\Leftrightarrow\left(x-1\right)\left(8x+24-x+1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(7x+25\right)=0\Rightarrow x=1\) (thỏa và 7x+25=0 loại do điều kiện....)

b nghiệm xấu quá để mình xem lại :v

\(\Leftrightarrow\sqrt{2x+6}+\sqrt{x-1}=2\sqrt{x+1}\)

\(\Leftrightarrow\sqrt{2x+6}-2\sqrt{2}+\sqrt{x-1}=2\sqrt{x+1}-2\sqrt{2}\)

\(\Leftrightarrow\frac{2\left(x-1\right)}{\sqrt{2x+6}+2\sqrt{2}}+\sqrt{x-1}=\frac{2\sqrt{x-1}}{\sqrt{x+1}+2\sqrt{2}}\)

\(\Leftrightarrow\frac{2\sqrt{x-1}}{\sqrt{2x+6}+2\sqrt{2}}+1=\frac{2\sqrt{x-1}}{\sqrt{x+1}+1\sqrt{2}}\)

đến đây thì chịu 

tìm đc 1 nghiệm là -1;1,nên bình phương lên

\(\sqrt{x^2+4}-2\sqrt{x+2}=0\)

\(\Leftrightarrow\sqrt{x^2+4}=2\sqrt{x+2}\)

\(\Leftrightarrow\sqrt{x^2+4}=\sqrt{4x+8}\)

\(\Leftrightarrow\sqrt{x^2+4}^2=\sqrt{4x+8}^2\)

\(\Leftrightarrow x^2+4=4x+8\)

\(\Leftrightarrow x^2-4x-4=0\)

\(\Delta=\left(-4\right)^2-4.1.\left(-4\right)=16+16=32\)

Vậy \(x_1=\frac{4+\sqrt{32}}{2}\);\(x_2=\frac{4-\sqrt{32}}{2}\)

P/S: Ko chắc

\(\sqrt{x^2+4}-2\sqrt{x+2}=0.\)

\(\Rightarrow\sqrt{x^2+4}=2\sqrt{x+2}\)

\(\Rightarrow x^2+4=2x+4\)

\(\Rightarrow x^2+4-2x-4=0.\)

\(\Rightarrow x^2-2x=0\)

\(\Rightarrow x\left(x-2\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x-2=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}}\)

Vậy .............

Study well 

chuyên toán thcsKhông biết bình phương à

b) X=5

a/ \(x^2-6x+9=4\sqrt{x^2-6x+6}\)

\(\Leftrightarrow\left(x^2-6x+6\right)-4\sqrt{x^2-6x+6}+3=0\)

Đặt \(a=\sqrt{x^2-6x+6},a\ge0\)

PT trên trở thành \(a^2-4a+3=0\Leftrightarrow\left(a-3\right)\left(a-1\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}a=1\\a=3\end{array}\right.\)

Tới đây bạn tự giải nhé ^^

b/ \(x^2+\sqrt{x^2+11}=31\Leftrightarrow\left(x^2+11\right)+\sqrt{x^2+11}-42=0\)

Đặt \(b=\sqrt{x^2+11},b>0\) thì pt trở thành

\(b^2+b-42=0\Leftrightarrow\left(b-6\right)\left(b+7\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}b=6\\b=-7\end{array}\right.\) (chú ý loại b = -7)

Tới đây bạn tự giải nhé ^^

TK MÌNH ĐI RỒI MÌNH GIẢI CHO.

cau a: 8x^3 -12x^2 + 6x + 1 =29

<=>8x^3 - 12x^2 + 6x - 28 =0

<=>(8x^3 - 16x^2)+(4x^2 - 8x)+(14x-28)=0

<=>8x^2 ( x-2) + 4x(x-2) + 14(x-2)=0

<=>(x-2)(8x^2 + 4x +14)=0

<=>8x^2 +4x +14 =0 <=> 8(x^2 +1/2 x +7/4)=0<=>(x^2 +2* x*1/4  + 1/16) +27/16 =0 <=>(x+ 1/4)^2=-27/16 (0xay ra) (loai)

=>(x-2)(8x^2 +4x+14)=0 <=> x-2=0 <=>x=2

Vay tap nghiem phuong trinh S={2}

b) x+3/x+2 +x+6/x+5=x+5/x+4 + x+4/x+3

=(x+3/x+2 -1) +(x+6/x+5 - 1)=(x+5/x+4 -1) +(x+4/x+3 -1)

 =1/x+2 +1/x+5 -1/x+4 -1/x+3 =0

x=1000

Lag tí -.-'

`ĐK:2<=x<=6`

BP 2 vế ta có:

`x-2+6-x+2\sqrt{(x-2)(6-x)}=x^2-8x+24`

`<=>4+2\sqrt{(x-2)(6-x)}=x^2-8x+24`

`<=>2\sqrt{(x-2)(6-x)}=x^2-8x+20`

`<=>2sqrt{-x^2+8x-12}=x^2-8x+20`

`<=>-x^2+8x-20+2sqrt{-x^2+8x-12}=0`

`<=>-x^2+8x-12+2sqrt{-x^2+8x-12}-8=0`

Đặt `sqrt{-x^2+8x-12}=a(a>=0)`

`pt<=>a^2+2a-8=0`

`<=>a=2(tm),a=-4(l)`

`<=>-x^2+8x-12=4`

`<=>x^2-8x+16=0`

`<=>(x-4)^2=0<=>x=4(tmđk)`

Vậy `S={4}`

Ghi thiếu đề bài nên tl lại 

`sqrt{x-2}+sqrt{6-x}=x^2-8x+16+2sqrt2`

Áp dụng BĐT bunhia ta có:

`sqrt{x-2}+sqrt{6-x}<=sqrt{(1+1)(x-2+6-x)}=2sqrt2`

`=>VT<=2sqrt2(1)`

Mặt khác:

`VP=x^2-8x+16+2sqrt2`

`=(x-4)^2+2sqrt2>=2sqrt2`

`=>VP>=2sqrt2(2)`

`(1)(2)=>VT=VP=2sqrt2`

`<=>x=4`

Vậy `S={4}`

`sqrt{x-2}+sqrt{6-x}=x^2-8x+2sqrt2`

Áp dụng BĐT bunhia ta có:

`sqrt{x-2}+sqrt{6-x}<=sqrt{(1+1)(x-2+6-x)}=2sqrt2`

`=>VT<=2sqrt2(1)`

Mặt khác:

`VP=x^2-8x+16+2sqrt2`

`=(x-4)^2+2sqrt2>=2sqrt2`

`=>VP>=2sqrt2(2)`

`(1)(2)=>VT=VP=2sqrt2`

`<=>x=4`

Vậy `S={4}`