Question

Find the roots a b y of x^3-11x^2+36x-36=0 if 2/b=1/a+1/y

Answer 1

Heya Mate

Let's do some crazy stuff

See the Rightmost no. there ? Looks cool right ? [ Probably Evident that 36 is the product of roots ]

Well, we just got a list of Factors to hit there and luckily "2" is a root that divides 36 and fortunately, 2 comes out to satisfy the Equation :

$= > (x - 2)( {x}^{2} - 9x + 18) = 0$

$= > (x - 2)(x - 3)(x - 6) = 0$

$= > x = 2 \: or \: 3 \: or \: 6$
Checking the configuration of a, b, y :

-> ( a , y ) = ( 2 , 6 ) and b = 3

^_^ Have a nice day