If (x + \(\frac{1}{x}\)) = 7.5, what is the value of (\(x^2+\frac{1}{x^2 }\))?

If x + \(\frac{1}{x}\), = 10 then find the value of \(\frac{7x}{x^2+1-8x}\)

If \(16x^4 +{{1} \over 16x^4}=14159,\)   then find the value of\(2x +{{1} \over 2x}.\)

If \(\dfrac{x^2}{y^2}+\dfrac{y^2}{x^2}=7\), What is the value of \(\dfrac{x^3}{y^3}+\dfrac{y^3}{x^3}\) is:

If (x - 1/x) = 7/3, what is the value of (x³ - 1/x³)

If \(a^2+b^2+\frac{1}{a^2}+\frac{1}{b^2}=4,a\neq0,b\neq0,\) then the value of a⁴ + b⁴ is:

If x + \(\frac{1}{x}\) = -13, what is the value of x⁴ + \(\frac{1}{x^4}\)?

If \(x +{{1} \over x}=2,\) then find the value of \((x^4 +{{4} \over (x)^4})(x^3- {{4} \over x^3}).\)

If p⁴ = 4354 - \(\frac{1}{p^4}\)then the value of p³ - \(\frac{1}{p^3}\)can be:

If \(a^2-4a+1=0\), then the value of \(a^2+a+\dfrac{1}{a}+\dfrac{1}{a^2}\) is:

If \((x -{1 \over x})=7.5\), what is the value of \((x^2 +{1 \over x^2})?\)

If \( (5y+\frac{5}{y})=11\), then find the value of\(\,(y^2+\frac{1}{y^2})\).

If x > 0, and x⁴ + \({{1} \over x^4}\)= 2207, what is the value of x⁷ + \({1 \over x^7}\) ?

If \(x = {\sqrt{5} -2\over \sqrt{5} +2}\), then the value of x² + x^-2 is :

If x + 1/x = 4, then find the value of x⁵ + x^-5.

If K + 1/K = 3, then what is the value of K³ + 1/K³?

Simplify  \({{x^2+2x+y^2} \over x^3-5x^2 }\)   if  \(x+{{y^2} \over x}=5\)

If x + \({1 \over x} = 8\), then find the value of 5/(x² - 8x +2)

If x > 0 and \(x^4+\frac{1}{x^4}=142\), what is the value of \(x^7+\frac{1}{x^7}\)?

k is a negative number such that k + k^-1 = - 2, then what is the value of (k² + 4k - 2)/(k² + k - 5) ?

If x² + \(\frac{1}{x^2}\)= 18, x > 0, then find the vale of x³ + \(\frac{1}{x^3}\).

If  \({{x=3+2\sqrt2,}}\)   x > 0, then the value of \(\sqrt x-{{1} \over \sqrt x}\) is :

If \(X-{{1} \over X}=13\),  what will be the value of \(X^4+{{1} \over X^4}=?\) 

If x + (1/x) = -14, and x < -1, what is the value of x² - (1/x²)?

What is the value of:

\((k-\frac{1}{k})(k^2+\frac{1}{k^2})(k^4+\frac{1}{k^4})(k^8+\frac{1}{k^{8}})(k^{16}+\frac{1}{k^{16}})(k^{32}+\frac{1}{k^{32}})\)

If \(x^2 + \frac{1}{x^2}\)= 7, and 0 < x < 1, then find the value of \(x^2 - \frac{1}{x^2}\).

If mx^m - nxⁿ = 0, then the value of \({{1} \over x^m+x^n}\) + \({{1} \over x^m-x^n}\) in terms of xⁿ is : 

Where x, m, n are > 0.

If k⁴ + (1/k⁴) = 47, then what is the value of k³ + (1/k³) ?

If x + \(\frac{2}{x}=1\), then the value of \(\frac{x^2+7x+2}{x^2+13x+2}\) is:

If \(p = 7+4\sqrt3,\) then what is the value of \({{p^6+p^4+p^2+1} \over p^3}\) ?

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

If \((4a+{{5} \over a}+5)=14\),  what is the value of \((16a^2+{{25} \over a^2})\)?

If \(x+{{1} \over x}=1\), then the value of x¹² + x⁹ + x⁶ + x³ + 1 is _______

If (x + \(\frac{1}{x}\)) = 7 and x > 1, what is the value of (x³ + \(\frac{1}{x^3}\))?

If \(x+{{1} \over x}=2\)cosθ, then  \(x^3+{{1} \over x^3}=?\)

If, for a non zero x, 5x² + 7x + 5 =0, then the value of \(x^3 + { {1} \over x^3}\) is:

The simplified form of (x + 2y)³ + (x - 2y)³ is :

If \(X+{{1} \over X}=-2,\) then what is the value of X¹⁷ +X^-17 + X¹² + X^-12  ? (x<0)

If \(x + {{1} \over x}\)= 2, then the value of  \(x^{57} + {{1} \over x^{57}}\) is :

Simplify [(81x² – 49y²) ÷ (9x + 7y)].

If a - \(\frac{1}{a}\) = 4, then the value of a + \(\frac{1}{a}\) is:

Find the degree of the polynomial 9x⁴ + 5x²y³ + 4.

Find (x + y)² - (x - y)².

Simplify the given expression.

(1 + x)³ + (1 - x)³ + (-2)³

If (x + 1/x) = 2, then find the value of (x³ + 1/x³) ÷ (x¹⁸ + 1/x¹⁸).

Given x + 1/x = 15, then find the value of 5x ÷ (5x² - 11x + 5).

Simplify the given expression.

(1 - x)² - (1 + x)²

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 \((y+\frac{1}{y}) = 8\), find the value of \((y^2+\frac{1}{y^2})\).