If (x + \(\frac{1}{x}\)) = 5\(\sqrt2\), and x > 1, what is the value of (x⁶ - \(\frac{1}{x^6}\)) ?

If \(x = \frac{1}{x-5}\) (x > 0),then the value of \(x + \frac1 x\) is :

If \({a^2}+\frac{1}{a^2}=\frac{7}{3}\), then what is the value of \({a^3}-\frac{1}{a^3}\)?

If ( z + \(\frac{1}{z}\) ) = 4, then what will be the value of \(\frac{1}{2}\) ( z² + \(\frac{1}{z^2}\) ) ?

If (x + \(\frac{1}{x}\)) = 5, what is the value of (x⁸ + \(\frac{1}{x^8}\))?

If x + \(\frac{1}{x}\) = 7 , Then the value of x² + \(\frac{1}{x^2}\) is :

If a = \(\frac{1}{a-\sqrt6}\) (a > 0), then the value of \((a+\frac 1 a)\) is:

If \(\left ( x+\frac{1}{x} \right )=2\sqrt{2}\), and x > 1, what is the value of \(\left ( x^6-\frac{1}{x^6} \right )\)?

If \(x + {1 \over x}\) =\(3 \sqrt{2}\), and x > 1, what is the value of (x⁸ - \(1 \over x^8\)) ?

If p = \(\frac{\sqrt 2 +1}{\sqrt 2-1}\) and q = \(\frac{\sqrt 2-1}{\sqrt 2+1}\) then find the value of \(\frac{p^2}{q}+\frac{q^2}{p}\).

If \((x+\frac{1}{x})=2\sqrt{2}\),  what is the value of \((x^6+\frac{1}{x^6})?\)

If (x − \(\frac{1}{x}\) ) = 6, and x > 0, find the value of (x² - \(\frac{1}{x^2}\)).

If \((2y+\frac{2}{y})=7\), find the value of \((y² + \frac{1}{y^2}).\)

If x > 0, and x⁴ + \(\frac{1}{x^4}\) = 254, what is the value of x⁵ + \(\frac{1}{x^5}\)?

If\(\left ( 3y-\frac{3}{y} \right )=5,\) find the value of \(\left ( y^2+\frac{1}{y^2} \right )\).

If \((x-\frac{1}{x})=2\sqrt{2}\) and x > 1, what is the value of \((x^6-\frac{1}{x^6})\)?

If (x + \(\frac{1}{x}\)) = 10, what is the value of (x⁴ + \(\frac{1}{x^4}\))?

If (x + \( {1{} \over x}\)) = 2, then x⁷ + 1/x⁷ =_______________.

If x + 1/x = √23, find the value of x³ + 1/x³.

If {√x + (1/√x)} = 3, then find the value of {x³ + (1/x³)} - 162.

If t = √5 + √7, find the value of t + \(1\over t\).

If 3x² + 3 + 5x = 0, find the value of x² + 1/x².

If x⁴ + x^-4 = 194, x > 0 then the value of (x – 2)² is:

If x + 1/x = -2, then what is the value of x¹⁶⁵¹ + 1/x³²⁶²?

If x² + 1/x² = 7, then what is the value of x⁵ + 1/x⁵, given that x > 0?

If (x + \(\frac{1}{x}\)) = \(\frac{11}{5}\), what is the value of (x³ + \(\frac{1}{x^3}\))?

If \(x + {1 \over x} = 3\), then \(x^6 + {1 \over x^6} \) is:

If (z + \(\frac{1}{z}\)) = 4, then what will be the value of \(\frac{1}{2}\) (z² + \(\frac{1}{z^2}\))?

If x + 1/(x - 4) = 8. Find the value of (x - 4)² + (1/(x - 4)²).

If 2x + 1/3x = 14 then find the value of (4x² + 1/9x²).

If 7b - (1/4b) = 7, then what is the value of 16b² + (1/49b²) ?

The sum of a natural number and its reciprocal is one-eight of 34. What is the product of the number and its square root?

If \(x+\frac{1}{x}=8\), find \(x^2-\frac{1}{x^2}\).

If \(x^2- 5\sqrt5 x + 1 = 0\), and x > 0, what is the value of \((x^3-{1\over x^3})\) ?

If \(\sqrt{x} -\frac{1}{\sqrt{x}}=\sqrt{7}\), then the value of \(x^2 + \frac{1}{x^2}\) ?

If x + 1/x = √2 then what will be the value of x⁶⁴ + x⁴⁸ + x³² + x¹⁶?

If {a + (1/a)} = 5, then find the value of: \(a^4+\frac{1}{a^4}\)

If a + 1/a = \(\sqrt{3}\) , then find a¹⁰² + a⁹⁶ + a¹⁰¹ + a⁹⁵ + a¹⁰⁰ + a⁹⁴ + a⁸⁴ + 3?

If {√x + (1/√x)} = 3, then find the value of {x³ + (1/x³)} - 162.

If 2x + 1/3x = 14 then find the value of (4x² + 1/9x²).

If \({x^{24} + 1}\over x^{12}\) = 7, then the value of \({x^{72} + 1}\over x^{36}\) is:

If \(\left(a + \frac{1}{a}\right)^2 = 3\) find the value of a²¹⁸ + a²¹² + a²⁴ + a¹⁸

If 3x² + 3 + 5x = 0, find the value of x² + 1/x².

If \(x = { \sqrt{2}}+1\) and \(y= {\sqrt{2} \over 3}\)  , then what is the value of\({{(x-2y-1)(x^2+4y^2+2xy-2x-2y+1)}}\)?

If \(x=\sqrt6+2\) and \(y=\sqrt6-2\), then what is the value of \(\left(\frac{x}{y}+\frac{y}{x}\right)^2-3\)?

If x² - 2√5x + 1 = 0, then which of the following is the value of x³ + \(\frac{1}{x^3}\)?

Which of the following statement is correct?

I. The value of 1002 –992 + 982 –972 + 962 –952 + 942 –932 + ……+ 222 –212 is 4840.

II. The value of \(\left(k^{2} + \frac{1}{k^{2}}\right) \left(k – \frac{1}{k}\right) \left(k^{4} + \frac{1}{k^{4}}\right) \left(k + \frac{1}{k}\right) \left(k^{4} + \frac{1}{k^{4}}\right) \left(k^{4} + \frac{1}{k^{4}}\right) \) is \(k^{16}-\frac{1}{k^{16}}\)

If \(x=\frac{\sqrt5-\sqrt4}{\sqrt5+\sqrt4}\) and \(y=\frac{\sqrt5+\sqrt4}{\sqrt5-\sqrt4}\) then the value of \(\frac{x^2-xy+y^2}{x^2+xy+y^2}\) =?

If \(\sqrt{x}\) - \(1\over\sqrt{x}\) = \(\sqrt{14}\), then the value of \(\sqrt{x^2+{1\over{x^2}}}\)is (correct to one decimal place):

If x⁴ - 3x² - 1 = 0, then the value of (x⁶ - 3x² + \(\frac{3}{x^2}-\frac{1}{x^6}\) + 1) is: