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If the following statement is True enter 1 and if False enter 0.
Let $x$ be a non-zero real number such that $x^{4} + \frac{1}{x^{4}}$ and $x^{5} + \frac{1}{x^{5}}$ are both rational numbers, then $x + \frac{1}{x}$ is a rational number.

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Similar Questions

Q1

If the following statement is True enter 1 and if False enter 0.

Let

x

be a non-zero real number such that

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

and

x^{5} + \frac{1}{x^{5}}

are both rational numbers, then

x + \frac{1}{x}

is a rational number.

View Solution

Q2

If

x

is a rational number satisfying

(1 - x) (1 + x + x^{2} + x^{3} + x^{4})

= \frac{31}{32} .

Then

1 + x + x^{2} + x^{3} + x^{4} + x^{5}

is

View Solution

Q3

If $(1 - x) (1 + x + x^{2} + x^{3} + x^{4})$ is $\frac{31}{32}$ and $x$ is a rational number. Find the value of $1 + x + x^{2} + x^{3} + x^{4} + x^{5}$ .

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Q4

x is a rational number satisfying (1-x) (1+x+x²+x³+x⁴) = .

Then 1+x+x²+x³+x⁴+X⁵ is

View Solution

Q5

Which of the following conditions imply that the real number

x

is rational
I.

x^{1 / 2}

is rational

II.

x^{2}

and

x^{5}

are rational

III.

x^{2}

and

x^{4}

are rational

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