Question

Tìm x biết \(\dfrac{1}{\left(X+29\right)^2}\)+\(\dfrac{1}{\left(X+30\right)^2}\)=5/4

Answer 1

đặt x+29=y

ta có :

\(\dfrac{1}{y^2}+\dfrac{1}{\left(y+1\right)^2}=\dfrac{5}{4}\)

\(\Leftrightarrow\dfrac{2y^2+2y+1}{y^4+2y^3+y^2}=\dfrac{5}{4}\)

\(\Leftrightarrow5y^4+10y^3-3y^2-8y-4=0\)

\(\Leftrightarrow\left(y-1\right)\left(5y^3+15y^2+12y+4\right)=0\)

\(\Leftrightarrow\left(y-1\right)\left(y+2\right)\left(5y^2+5y+2\right)=0\)

\(\left[{}\begin{matrix}y-1=0\Leftrightarrow y=1\Rightarrow x+29=1\Leftrightarrow x=-28\\y+2=0\Leftrightarrow y=-2\Rightarrow x+29=-2\Leftrightarrow x=-31\\5y^2+5y+2=0\left(loại\right)\end{matrix}\right.\)

vậy, S={-31;-28}