If f is an even function defined on the interval (-5,5), then the real values of x, satisfying the equation f(x)=f(x+1x+2) are
−3±√52
Given that f(x)=f(x+1x+2) and f is an even function
∴f(x)=f(−x)=f(−x+1−x+2)⇒x=−x+1−x+2 ⇒x2−3x+1=0 ⇒x=3±√52Also f(x)=f(x+1x+2)=f(−x)⇒ x+1x+2=−x⇒ x2+3x+1=0 ⇒x=−3±√52∴ Four values of x are
3+√52, 3−√52, −3+√52, −3−√52