Question

if x-y=3 & xy=27.
then find the value of (x+y)³

Answer 1

Eqns; x - y = 3 ..........................(i)

          xy = 27 ...........................(ii)

from eqn (ii)

x = 27/y

sub this value into eqn (i)

27/y - y = 3

27 - y^2 = 3y

y^2 + 3y - 27 = 0

from y = {-b +/- (b^2 -4ac)^1/2}/2a

y = {-3 +/- (9 + 108)}/2

y = (-3 +/ 10.82)/2

either

y = -6.91  ......... or...........   3.91

from { x = 27/y}

either

x = -3.91(for y = -6.91)  .................. or ...............  6.91(fro y = 3.91)

(x + y)^3 = (-3.91 - 6.91)^3

= -1266.72

or 

(x + y)^3 =(3.91 + 6.91)^3

=1266.72

therefore

(x + y)^3 = 1266.72 or -1266.72 {correct to 2dps}