Question

Solve the following quadratic equations by factorization:

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

Answer 1

We have been given

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

`x^2+ax+1/ax+1=0`

`x(x+a)+1/a(x+a)=0`

`(x+1/a)(x+a)=0`

Therefore,

`x+1/a=0`

`x=-1/a`

or,

x + a = 0

x = -a

Hence, `x=-1/a` or x = -a.