Question

tim x biet

(x² - 4)( x² - 10) = 72

Answer 1

\(\left(x^2-4\right)\left(x^2-10\right)=72\)

<=> \(x^4-14x^2+40-72=0\)

<=> \(x^4-14x^2-32=0\)

<=> \(\left(x^2-16\right)\left(x^2+2\right)=0\)

<=> \(\left[\begin{array}{nghiempt}x^2-16=0\\x^2+2=0\end{array}\right.\)=> x=\(\pm\)4

vậy tập nghiệm S={4;-4}

Answer 2

\(\left(x^2-4\right)\left(x^2-10\right)=72\)
\(\Leftrightarrow x^4-10x^2-4x^2+40=72\)
\(\Leftrightarrow x^4-14x^2+40-72=0\)
\(\Leftrightarrow x^4-14x^2-32=0\)
\(\Leftrightarrow x^4+2x^2-16x^2-32=0\)
\(\Leftrightarrow x^2\left(x^2+2\right)-16\left(x^2+2\right)=0\)
\(\Leftrightarrow\left(x^2+2\right)\left(x^2-16\right)=0\)
\(\Leftrightarrow\left(x^2+2\right)\left(x^2-4^2\right)=0\)
\(\Leftrightarrow\left(x^2+2\right)\left(x-4\right)\left(x+4\right)=0\left(1\right)\)
\(Có:x^2\ge0\)\(\text{ với mọi x}\)
\(\Rightarrow x^2+2\ge0+2=2\ne0\text{ với mọi x}\)
\(\left(1\right)\Leftrightarrow\left[\begin{array}{nghiempt}x-4=0\\x+4=0\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=4\\x=-4\end{array}\right.\)
\(\text{Vậy }x=\pm4\)
 

Answer 3

\(\left(x^2-4\right)\left(x^2-10\right)=72\)

\(\Leftrightarrow x^4-14x^2+40=72\)

\(\Leftrightarrow x^4-14x^2-32=0\)

\(\Leftrightarrow\left(x-4\right)\left(x^3+4x^2+2x+8\right)=0\)

\(\Leftrightarrow\begin{cases}\left(x+4\right)=0\\\left(x-4\right)=0\\\left(x^2+2\right)=0\left(loại\right)\end{cases}\)Vậy \(x\in\left\{-4;4\right\}\)