If $$ {x+{1\over x}=7}$$ then $$ {x^{2}+{1\over {x^{2}}}=?}$$

If 4x² + y² = 40 and xy = 6, then find the value of 2x + y.

If (x + 6y) = 8, and xy = 2, where x > O, what is the value of (x³+216y³)?

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) 12x² + 11x + 2 = 0
(ii) 12y²+ 7y + 1 = 0

What is the value of a²+b²+c²-2ab-2bc+2ca?

If x²+4y²=17 and xy=2, where x>0,y>0, then what is the value of x³+8y³?

If x = z = 225 and y = 226 then the value of : x³ + y³ + z³ – 3xyz is

If a ≠ b, then which of the following statement is true ?