Question Number 11515 by @ANTARES_VY last updated on 27/Mar/17

(((4+x)/x))^(1/5) −(((4−6x)/x))^(1/5) =1.  x_1 +x_2 =?

Answered by ajfour last updated on 27/Mar/17

x=(4/(15))

Commented byajfour last updated on 27/Mar/17

(√((4+x)/x))+(√((4−6x)/x))=1   ....(i)  let  (√((4+x)/x))−(√((4−6x)/x))=a    ...(ii)  multiplying above two equations  (((4+x)/x) )− (((4−6x)/x) )=a  ⇒  7=a  adding  (i) and (ii):  2(√((4+x)/x)) = a+1 = 8  (as a=7 )  ⇒  ((4+x)/x) =16  ⇒ 15x =4     x = (4/(15))  .

Commented bymrW1 last updated on 27/Mar/17

in the equation it is not (√(   )), but  ^5 (√(  )).

Commented by@ANTARES_VY last updated on 27/Mar/17

understand  solved

Commented bychux last updated on 27/Mar/17

please which keyboard editor do   you use?

Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 29/Mar/17

l_ et:((4+x)/x)=a^5 ⇒(4/x)+1=a^5 ⇒(4/x)−6=a^5 −7  a−((a^5 −7))^(1/5) =1⇒(a−1)^5 =a^5 −7  a^5 −5a^4 +10a^3 −10a^2 +5a−1=a^5 −7  5a^4 −10a^3 +10a^2 −5a−6=0  ⇒a=1.47⇒((4+x)/x)=(1.47)^5 =6.86  (4/x)=5.86⇒x=(4/(5.86))=.682  .

Commented byb.e.h.i.8.3.4.1.7@gmail.com last updated on 29/Mar/17

Commented byb.e.h.i.8.3.4.1.7@gmail.com last updated on 29/Mar/17