If x= 5 + 2 5 - 2 , y= 5 - 2 5 + 2 , then 3 x^2+4 x y-3 y^2 is equal to

Step-by-step solution

Given that, y= 5 - 2 5 + 2 and x= 5 + 2 5 - 2 array ll & y= 1 x & x y=1 array aligned & 3 x^2+4 x y-3 y^2=3(x-y) (x+y)+4 x y aligned aligned &=3 ( 5 + 2 5 - 2 - 5 - 2 5 + 2 ) ( 5 + 2 5 - 2 + 5 - 2 5 + 2 )+4 aligned aligned & =3 [ ( 5 + 2 )^2-( 5 - 2 )^2 (5-2)(5-2) ] [( 5 + 2 )^2+( 5 - 2 )^2 ]+4 & = 1 3 4 10 2(5+2)+4 & = 56 3 10 +4 & = 1 3 (56 10 +12) aligned