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

If x+y+z=10, x²+y²+z²=30, then the value of x³+y³+z³-3xyz is _________.

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

Simplify the following expression.

$${\left({375+125} \right)^2-\left({125-375} \right)^2}\over 375×375-125×125$$

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

If P = 99, then the value of P(P²+3P+3) is

$$ {1\over {^3\sqrt{4}+{^3\sqrt{2}}}+1}=a^3\sqrt{4}+ b^3\sqrt{2}+c $$ and a, b, c are rational numbers, then a + b + c is equal to

 If 3x²-5x+1=0, then the value of ( $$x^2+{1\over 9x^2}$$) is