Question

factorise the following expression: x^2-[a/b+b/a]x+1​

Answer 1

Let --> y = ( a / ( a + b ) ) ;

--> x² + [ y + 1/y ]x + 1 = 0

=> yx² + [ y² + 1 ] x + y = 0

=> yx² + y²x + x + y = 0

=> [ yx + 1 ][ x + y ] = 0

=> x = [ - 1 / y ]  || x = - y

=> x = [ ( - a - b ) / a ] || x = [ -a / ( a + b ) ]