Question

The sum of a number and its reciprocal is 2 1/12. Find the number.

Answer 1

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Answer:

Reciprocal is 25/12

So, the number is

12/25

Answer 2

The number is $\bold{\frac{3}{4} \:or\:\frac{4}{3} }$.

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Let's understand the concept of reciprocal of number:

What is the reciprocal of a number?

The reciprocal of a number is one divided by that number.

• To get the reciprocal of a whole number, we rewrite the number as a fraction and then swap the numerator and denominator. For eg. reciprocal of 2 is $\frac{1}{2}$.

• To get the reciprocal of a fraction, we swap the numerator and denominator. For eg. reciprocal of $\frac{5}{2}$ is $\frac{2}{5}$.

• To get the reciprocal of a mixed fraction, we rewrite the mixed fraction into improper fractions and then swap the numerator and denominator. For eg. reciprocal of $1\frac{1}{2}$ i.e., $\frac{3}{2}$ is $\frac{2}{3}$.

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Let's solve the given problem:

Let's say "x" is the number.

So, its reciprocal will be " $\bold{\frac{1}{x} }$ ".

The sum of a number and its reciprocal is 2 1/12. So we can from the equation as,

$x + \frac{1}{x} = 2\frac{1}{12}$

$\implies x + \frac{1}{x} = \frac{25}{12}$

• taking the L.C.M. on the left side

$\implies \frac{x^2 + 1}{x} = \frac{25}{12}$

• cross-multiplying both sides

$\implies 12x^2 + 12= 25x$

$\implies 12x^2 - 25x + 12= 0$

• applying middle term splitting

$\implies 12x^2 - 16x - 9x + 12= 0$

$\implies 4x(3x - 4) -3(3x - 4) = 0$

$\implies (4x - 3) (3x - 4) = 0$

• equation both the factors to get zero

$\implies (4x - 3) = 0 \:or\: (3x - 4) = 0$

$\implies x = \frac{3}{4} \:or\: x = \frac{4}{3}$

Thus, the number is $\bold{\frac{3}{4} \:or\:\frac{4}{3} }$.

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