Question

Solve the following quadratic equations by factorization: $x^{2}+(a+\frac{1}{a})x+1=0$

Answer 1

SOLUTION :  

Given : x² + (a + 1/a)x + 1 = 0

x² + ax + x/a + 1 = 0

x(x + a) + 1/a (x + a) = 0          [ 1/a × a = 1]

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

(x + 1/a)  = 0  or  (x + a) = 0

[Equate each factor to zero]

x = - 1/a  or  x = - a  

Hence, the roots of the quadratic equation x² + (a + 1/a)x + 1 = 0 are -1/a  & - a .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Solution :

$x^{2}+(a+\frac{1}{a})x+1=0$

=> x² + ( a + 1/a )x + a × 1/a = 0

************************************

We know the algebraic identity :

x² + ( m + n )x + mn = ( x + m )( x + n )

**************************************

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

=> x + a = 0 or x + 1/a = 0

=> x = -a or x = -1/a

Therefore,

x = -a or x = -1/a

••••