\(x^4-2x^2-144x-1295=0\)

\(\Leftrightarrow x^4-7x^3+7x^3-49x^2+47x^2-329x+185x-1295=0\)

\(\Leftrightarrow x^3\left(x-7\right)+7x^2\left(x-7\right)+47x\left(x-7\right)+185\left(x-7\right)=0\)

\(\Leftrightarrow\left(x-7\right)\left(x^3+7x^2+47x+185\right)=0\)

\(\Leftrightarrow\left(x-7\right)\left(x^3+5x^2+2x^2+10x+37x+185\right)=0\)

\(\Leftrightarrow\left(x-7\right)\left[x^2\left(x+5\right)+2x\left(x+5\right)+37\left(x+5\right)\right]=0\)

\(\Leftrightarrow\left(x-7\right)\left(x+5\right)\left(x^2+2x+37\right)=0\)

\(\Leftrightarrow\)\(x-7=0\)

hoặc   \(x+5=0\)

hoặc   \(x^2+2x+37=0\)

\(\Leftrightarrow\)\(x=7\)(tm)

hoặc   \(x=-5\)(tm)

hoặc \(\left(x+1\right)^2+36=0\)(ktm)

Vậy tập nghiệm của phương trình là \(S=\left\{7;-5\right\}\)

=>x^4+2x^2+1-4x^2-144x-1296=0

=>(x^2+1)^2-(2x+36)^2=0

=>(x^2+1-2x-36)(x^2+1+2x+36)=0

=>x^2-2x-35=0

=>(x-7)(x+5)=0

=>x=7 hoặc x=-5

\(x^4-2x^2-144x-1295=0\)

\(\Leftrightarrow\left(x^4+2x^2+1\right)-\left(4x^2+144x+1296\right)=0\)

\(\Leftrightarrow\left(x^2+1\right)^2-\left(2x+36\right)^2=0\)

\(\Leftrightarrow\left(x^2+1+2x+36\right)\left[x^2+1-\left(2x+36\right)\right]=0\)

\(\Leftrightarrow\left(x^2+2x+37\right)\left(x^2-2x-35\right)=0\)

\(\Leftrightarrow\left(x^2+5x-7x-35\right)\left(x^2+2x+1+36\right)=0\)

\(\Leftrightarrow\left[x\left(x+5\right)-7\left(x+5\right)\right]\left[\left(x+1\right)^2+36\right]=0\)

\(\Leftrightarrow\left(x+5\right)\left(x-7\right)\left[\left(x+1\right)^2+36\right]=0\)

Dễ thấy:\(\left(x+1\right)^2+36\ge36>0\forall x\) (vô nghiệm)

\(\Rightarrow\left[{}\begin{matrix}x+5=0\\x-7=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=-5\\x=7\end{matrix}\right.\)

28 BN NHÉ TÍCH ĐI

tk ủng hộ mk nha mọi người ai tk mk mk tk lại 3 tk

pt <=> (x^4-5x^3)+(5x^3-25x^2)+(23x^2-115x)+(259x-1295) = 0

<=> (x-5).(x^3+5x^2+23x+259) = 0

<=> (x-5).[(x^3+7x^2)-(2x^2+14x)+(37x+259)] = 0

<=> (x-5).(x+7).(x^2-2x+37) = 0

<=> (x-5).(x+7) = 0 ( vì x^2-2x+37 > 0 )

<=> x-5=0 hoặc x+7=0

<=> x=5 hoặc x=-7

Vậy .........

Tk mk nha

Bài làm

x⁴ - 2x² - 144x - 1295 = 0

<=> x⁴ + 2x² - 4x² - 144x - 1296 + 1 = 0

<=> ( x⁴ + 2x² + 1 ) - ( 4x² + 144x + 1296 ) = 0

<=> ( x² + 1 )² - ( 2x + 36 )² = 0

<=> ( x² + 1 - 2x - 36 )( x² + 1 + 2x + 36 ) = 0

<=> ( x² - 2x - 35 )( x² + 2x + 37 ) = 0

<=> ( x² + 5x - 7x - 35 ) ( x² + 2x + 1 + 36 ) = 0

<=> [ x( x + 5 ) - 7( x + 5 ) ][ ( x² + 2x + 1 ) + 36 ] = 0

<=> ( x + 5 )( x - 7 )[ ( x + 1 )² + 36 ] = 0

Ta có: ( x + 1 )² \(\ge\)0

<=> ( x + 1 )² + 36 \(\ge\)36

=> ( x + 5 )( x - 7 ) = 0

<=> \(\left[{}\begin{matrix}x+5=0\\x-7=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=-5\\x=7\end{matrix}\right.\)

Vậy tập nghiệm phương trình trên là: S = { -5; 7 }

# Học tốt #

Bài này không nhất thiết phải đặt ẩn phụ nên mình giải luôn nhé.

\(x^4-2x^2-144x-1295=0\\ \Leftrightarrow x^4-4x^2+2x^2-144x+1-1296=0\\\Leftrightarrow \left(x^4+2x^2+1\right)-\left(4x^2+144x+1296\right)=0\\ \Leftrightarrow\left(x^2+1\right)^2-\left(2x+36\right)=0\\ \Leftrightarrow\left(x^2+1-2x-36\right)\left(x^2+1+2x+36\right)=0\\ \Leftrightarrow\left(x^2-2x-35\right)\left[\left(x+1\right)^2+36\right]=0\\\Leftrightarrow \left(x^2+5x-7x-35\right)\left[\left(x+1\right)^2+36\right]=0\\ \Rightarrow\left(x+5\right)\left(x-7\right)\left[\left(x+1\right)^2+36\right]=0\\ \Leftrightarrow\left[{}\begin{matrix}x+5=0\\x-7=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-5\\x=7\end{matrix}\right.\left(vi\left[\left(x+1\right)^2+36>0\forall\right]x\right)\)

Vậy tập nghiệm của phương trình trên là \(S=\left\{-5;7\right\}\)

$x^4-2x^2-144x-1295=0$

$\iff \left(x^4+2x^2+1\right)-\left(4x^2+144x+1296\right)=0$

$\iff {\left(x^2+1\right)}^2-{\left(2x+36\right)}^2=0$

$\iff \left(x^2+1+2x+36\right)\left[x^2+1-\left(2x+36\right)\right]=0$

$\iff \left(x^2+2x+37\right)\left(x^2-2x-35\right)=0$

$\iff \left(x^2+5x-7x-35\right)\left(x^2+2x+1+36\right)=0$

$\iff \left[x\left(x+5\right)-7\left(x+5\right)\right]\left[{\left(x+1\right)}^2+36\right]=0$

$\iff \left(x+5\right)\left(x-7\right)\left[{\left(x+1\right)}^2+36\right]=0$

Dễ thấy:${\left(x+1\right)}^2+36\ge 36>0\forall x$ (vô nghiệm)

$\Rightarrow [\begin{array}{c}x+5=0\\ x-7=0\end{array}$$\Rightarrow [\begin{array}{c}x=-5\\ x=7\end{array}$

\(x^4-2x^2-144x-1295=\left(x+5\right)\left(x-7\right)\left(x^2+2x+37\right)\)

1295^2 - 144 = 1677025 - 144 = 1676881 

(x+y) ^ 4 = (x+y) x (x+y) x (x+y) x (x+y) = 4(x+y) + x^4 + y^4 = 4 + 4 + 4 = 4 x 3 = 12