If #x^2 + 1/x^2 = 27#. Then find #x-1/x# ?

If #x^2 + 1/x^2 = 27#. Then find #x-1/x#

2 Answers
Jan 27, 2018

#x-1/x = +-5#

Explanation:

just expand, rearrange n substitute,!
#(x-1/x)^2#

#=x^2 -2*x*1/x +(1/x)^2#

#=x^2 -2+(1/x)^2#

#=x^2+1/x^2-2#

since we have the value of #x^2+1/x^2# as #27#,

#=27-2#

#=25#

#=>(x-1/x)^2 = 25#

#=>x-1/x = +-5#

-Sahar

Jan 27, 2018

#x-1/x=+-5#

Explanation:

#"note that "(x-1/x)^2=x^2-2+1/x^2#

#rArrx^2-2+1/x^2=27-2=25#

#rArr(x-1/x)^2=25#

#color(blue)"take the square root of both sides"#

#rArrx-1/x=+-5larrcolor(blue)"note plus or minus"#