Question

A number added to twice its reciprocal is equal to 11 over 3. What is the number? Show the solution

Answer 1

Hey .......!!


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Let the number be x

According to the question !

$x + 2 (\frac{1}{x}) = \frac{11}{3} \\ \\ {x}^{2} + 2 = \frac{11}{3}(x) \\ \\ 3{x}^{2} + 6 = 11x \\ \\ 3{x}^{2} - 11x + 6 = 0 \\ \\ 3x - 2 ( x - 3 ) \\ \\ x = \frac{-2}{3} , x = + 3$

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Answer 2

Answer:

Required number is 2/3 or 3.

Step-by-step explanation:

Given,a number added to twice its reciprocal is equal to 11 over 3.

Let the number be x.

x is added to twice its reciprocal.

Now question is what is reciprocal of number?

If p is a number then reciprocal of p is $\frac{1}{p}$

For example reciprocal of 2 is $\frac{1}{2}$

Here number is x

So, reciprocal of x is $\frac{1}{x}$

Given,the number added to twice its reciprocal is equal to 11 over 3

According to question,

$x+\frac{2}{x} = \frac{11}{3}$

3(x² + 2) =11x

3x² − 11x + 6 = 0

3x² − 9x − 2x + 6 = 0

3x(x − 3) − 2(x − 3) = 0

(3x − 2)(x − 3) = 0

If product of two numbers is zero then they are separately zero.

So,(3x-2)=0

x=2/3

and x-3=0

x=3

This is a problem of Algebra.

Some important Algebra formula,

a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)