Question Number 104621 by ajfour last updated on 22/Jul/20

(1/((1−x)^2 ))−(4/((1+x)^2 ))=1

Answered by prakash jain last updated on 22/Jul/20

(1+x)^2 −4(1−x)^2 =(1−2x+x^2 )(1+2x+x^2 )  −3x^2 +10x−3=     x^4 −2x^2 +1  x^4 +x^2 −10x+4=0  (x^2 +2)^2 −3x^2 −10x=0  (x^2 +2)^2 +2k(x^2 +2)+k^2         =(3+2k)x^2 +10x+(k^2 +4k)  (x^2 +2+k)^2 =(3+2k)x^2 +10x+(k^2 +4k)  10=2(√((3+2k)(k^2 +4k))) ⇒k=1  (x^2 +3)^2 =5(x+1)^2   Equation can be splitted into  2 quadratic at this point.

Commented byajfour last updated on 24/Jul/20

thanks! prakash Sir, but generally  finding k , would require, solving a  cubic, i believe..

Commented byprakash jain last updated on 24/Jul/20

I found as solution was obvious.  You are right.