If x/(x^2+3x+1)=a Then find the value of X^2/(x^4+3x^2+1). ?

Question

1631 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-17T19:19:34

# a^2/(1-6a+10a^2)#.

Given that, #x/(x^2+3x+1)=a#.

#:. (x^2+3x+1)/x=1/a, i.e., x^2/x+(3x)/x+1/x=1/a, or, #

# x+3+1/x=1/a#.

#:. x+1/x=1/a-3#.

#:. (x+1/x)^2=(1/a-3)^2=(1-3a)^2/a^2..."[Squaring]"#.

#:. x^2+2+1/x^2=(1-6a+9a^2)/a^2#.

#"Adding 1, "x^2+3+1/x^2=(1-6a+9a^2)/a^2+1, i.e., #

# (x^4+3x^2+1)/x^2=(1-6a+10a^2)/a^2#.

#:. x^2/(x^4+3x^2+1)=a^2/(1-6a+10a^2)#, is the desired value!

Feel the Joy of Maths.!