If 2x – y = 2 and xy =  \(\frac{3}{2}\) , then what is the value of x ³–  \(\frac{{{y^3}}}{8}\) ?

If \((x + {1\over x}) = \sqrt6\), and x > 1, what is the value of \((x^8 - {1 \over x^8})\)?

If (a³ + b³ + c³ - 3abc) = 405, and (a - b)² + (b - c)² + (c -a)² = 54, find the value of (a + b + c).

Which of the following statement is correct?

I. If x = 12, y = -2 and z = -10, then x³ + y³ + z³ = 720

II. If x + y = 48 and 4xy = 128, then s the value of 4x² + 4y² is 8960

If m + \({{1} \over m \ - \ 2}\) = 4, then find the value of (m - 2)² + \({{1} \over (m \ - \ 2)^2}\).

If 5x - \({{5} \over x}\) + 6 = 0, then x² + \({{1} \over x^{2}}\) is:

If a = 26 and b = 22, then the value of \({{a^3 \ - \ b^{3}} \over a^2 \ - \ b^{2}}\) - \({{3ab} \over a \ + \ b}\) is ______.

If a² + b² + c² = ab + bc + ac, then the value of \(\rm \frac{11 a^4+13 b^4+17 c^4}{17 a^2 b^2+9 b^2 c^2+15 c^2 a^2}\) is ?

If \((x+\frac{1}{x})\) = 5, and x > 1, what is the value of \((x^8-\frac{1}{x^8} )\)?

In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. x² – 26x + 165 = 0

II. y² – 38y + 357 = 0

Factorize the following:

(x ²- 6xy + 9y ²) - 25

If P and Q are the points on the line Joining A(-2, 5) and B(3, 1) such that

AP = PQ = QB, then the mid point of PQ is 

If a number and its reciprocal added it becomes 6, then what will be sum of its square and square of its reciprocal?