Question

# 7. Which of the following imply that the real number x must be rational? I. x, x7are both rational II. x, x are both rational II. x5, x are both rational O I, Il only O I, IlIl only O II, Il only O Il only O None of these combinations Tagged in

Rational functions
7. Which of the following imply that the real number x must be rational? I. x, x7are both rational II. x, x are both rational II. x5, x are both rational
O I, Il only
O I, IlIl only
O II, Il only
O Il only
O None of these combinations Tagged in

2020-11-02
Given
The real number x be the rational number .
Let $$x=p/q$$ and n be the any exponent of x .
$$x^n=(p/q)^n$$
$$=(p/q)(p/q)(p/q)(p/q)...(p/q)$$
$$x^n=(p^n/q^n)$$
Here multiplication of rational number is rational number .
By using above expression
$$x^5,x^6,x^7,x^8$$ are rational numbers .
There is no option with all conditions.
Therefore , The none of these combination is correct option.