Question

find x : x^2(x+1)^2+x^2=3(x+1)^2

Answer 1

x2+x2(x+1)2=3x2+x2(x+1)2=3

x2+(xx+1)2=3x2+(xx+1)2=3

x2+(1−1x+1)2=3x2+(1−1x+1)2=3

x2+1−2x+1+(1x+1)2=3x2+1−2x+1+(1x+1)2=3

x2+2−2x+1+(1x+1)2=4x2+2−2x+1+(1x+1)2=4

x2+2x+2−2x+1+(1x+1)2=4x2+2x+2−2x+1+(1x+1)2=4

x2+2xx+1+(1x+1)2=4x2+2xx+1+(1x+1)2=4

(x+1x+1)2=4(x+1x+1)2=4

x+1x+1=±2x+1x+1=±2

x=1±5√2x=1±52, −3±i3√2