Question

Solve the following quadratic equation for x:

`x^2+(a/(a+b)+(a+b)/a)x+1=0`

Answer 1

Given: 

`x^2+(a/(a+b)+(a+b)/a)x+1=0`

Let `a/(a+b)`be t

Thus, the equation becomes 

`x^2+(t+1/t)x+1=0`

⇒x²+(t+`1/t`)x+1=0

⇒x²+(`(t^2+1)/1`)x+1=0

⇒tx²+(t²+1)x+t=0

⇒tx²+t²x+x+t=0

⇒(tx²+t²x)+(x+t)=0

⇒tx(x+t)+1(x+t)=0

⇒(tx+1)(x+t)=0

⇒tx+1=0, x+t=0

`=>x=(-1)/t,x= -t`

`=>x = (-1)/(a/(a+b)), x = -a/(a+b)`

 `=>x= -(a+b)/a, x= -a/(a+b)`