Simplify the following expression.

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

if x⁴+y⁴+x²y²=21 and x²+y²-xy=7, then what is the value of  $${x\over y}+{y\over x}=?$$

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 m = – 4, n = – 2, then the value of m³ – 3m² + 3m + 3n + 3n² + n³ is

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

P = 12xy – 10y² – 18x²,

Q = 14x² + 12y² + 9xy, and

R = 5y² – x² + xy

then (P + Q) – R =

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

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