Practice30 Create account

If $x = 7 + 43$ , find the value of $x + \frac{1}{x}$ .
(Hint: rationalise $\frac{1}{x}$ first.)

Class 9Rational and Irrational NumbersNumber Systems

A14
B28
C13
D15

Step-by-Step Solution

\frac{1}{x} = \frac{1}{7 + 4 3}

. Multiply by conjugate

(7 - 43)

: denominator = 49 - 48 = 1, so

\frac{1}{x} = 7 - 43

. Then

x + \frac{1}{x} = (7 + 43) + (7 - 43) = 14

.

Answer: A) 14

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Rational and Irrational Numbers practice questions

More Class 9 Rational and Irrational Numbers practice

A student claims √2 is rational and writes √2 = a/b in lowest terms. Squaring gives 2 =…On a spiral construction (the 'square root spiral'), each new right triangle adds a…Which of the following is a rational number?Which of the following is equal to a terminating decimal?How many rational numbers lie between 1 and 2?