Simplify the following expression.

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

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

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

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

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:

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