If a + b = 1 and a³ + b³ + 3ab = k, then the value of k is

If $$x+{1\over x}=c{1\over c}$$ then the value of x

if x+y =3 and $${1\over x}+{1\over y}= -{3\over 10}$$ then the value of (x²+y²) is :

Directions: In each of these questions, two equations (i) and (ii) are given, you have to solve both the equations and give answer accordingly.

(i) 21x² + 10x + 1 = 0
 (ii) 24y²+ 26y + 5 = 0

If 9x² + y² = 37 and xy = 2, x, y>0, then the value of (27x³+ y³) is:

P = 12xy – 10y² – 18x²,

Q = 14x² + 12y² + 9xy, and

R = 5y² – x² + xy

then (P + Q) – R =

Directions: In each of these questions, two equations (i) and (ii) are given, you have to solve both the equations and give answer accordingly.

(i) 3x² + 11x + 10 = 0
 (ii) 2y² + 11y + 14 = 0

 if $$x^4+{16\over x^4}=15617, x>0$$ then find the value of $$x+{2\over x}$$