help quadratic

Note     1/a^2  + 1/b^2 =      [a^2 + b^2 ] / [ ab ] ^2

The sum of the roots =   11/5  =  a + b

Square both sides

121/25 =  a^2 + 2ab + b^2

The product of the roots =    4/5 = ab     so.....2ab =  8/5        and [ab]^2 = 16/25

So 

121/25 = a^2 + 2(4/5) + b^2

121/25 = a^2 + 8/5 + b^2

121/25  - 8/5 = a^2 + b^2

121/25 - 8/5 = a^2 + b^2

121/25 - 40/25 = a^2 + b^2

81/25 =  a^2 + b^2

So

1/a^2  + 1/b^2 =   [ 81/25] / [ 16/25 ] =    81 / 16