If x = and y = find the value of x 2 + y 2 + xy .

Step-by-step solution

Consider x = = (Rationalising the denominator) = Similarly, y = Now, xy = and x + y = Squaring both sides, we get ( x + y ) 2 = 36 x 2 + y 2 + 2 xy = 36 x 2 + y 2 + 2 × 1 = 36 x 2 + y 2 = 34 Hence, x 2 + y 2 + xy = 34 + 1 = 35