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Algebraic Identities

If x 4+1 x 4=...

Question

If $x^{4} + \frac{1}{x^{4}} = 194,$ then $x^{3} + \frac{1}{x^{3}} =$

(a) 76

(b) 52

(c) 64

(d) none of these

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Solution

Given

Using identity

Here,

Again using identity

Here

Substituting

Using identity

Here

Hence the value of is

The correct choice is (b).

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Similar questions

x^{4} + \frac{1}{x^{4}} = 194,

x^{3} + \frac{1}{x^{3}}, x^{2} + \frac{1}{x^{2}}

x + \frac{1}{x}

x^{4} + \frac{1}{x^{4}} = 194

, find the value of

x^{3} + \frac{1}{x^{3}}

.

If $x + \frac{1}{x} = 3$ , calculate $x^{2} + \frac{1}{x^{2}}, x^{3} + \frac{1}{x^{3}}$ and $x^{4} + \frac{1}{x^{4}}$

x^{4} + \frac{1}{x^{4}} = 119

, find the value of

x^{3} - \frac{1}{x^{3}}

x_{1}, x_{2}, x_{3}, x_{4}

are roots of the equation

x^{4} - x^{3} s i n 2 β + x^{2} c o s 2 β - x c o s β - s i n β = 0

t a n^{- 1} x_{1} + t a n^{- 1} x_{2} + t a n^{- 1} x_{3} + t a n^{- 1} x_{4} =

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