Question

The sum of number and it's reciprocal is 10/3 ,then the number is. ​

Answer 1

Step-by-step explanation:

x+1/x=10/3

By taking LCM

x²+1/x=10/3

By cross multiplication

10x=3x²+3

3x²-10x+3=0

By spliting the middle term

3x²-x-9x+3=0

x(3x-1)-3(3x-1)=0

(x-3)(3x-1)=0

x=3 , x= 1/3

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Answer 2

Given :-

• The sum of a number and it's reciprocal is 10/3.

To find :-

• The number = ?

Solution :-

Let the required number be x

Then,

$\rm\:x+\dfrac{1}{x}=\dfrac{10}{3}$

$\rm\longrightarrow\:\dfrac{{x}^{2}+1}{x}=\dfrac{10}{3}$

$\rm\longrightarrow\:3({x}^{2}+1)=x\times\:10$

$\rm\longrightarrow\:3({x}^{2}+1)=10x$

$\rm\longrightarrow\:{3x}^{2}-10x+3=0$

$\rm\longrightarrow\:{3x}^{2}-9x-x+3=0$

$\rm\longrightarrow\:3x(x-3)-1(x-3)=0$

$\rm\longrightarrow\:(x-3)(3x-1)=0$

Now,

$\rm\:x-3=0$

$\rm\longrightarrow\:x=0+3$

$\rm\longrightarrow\:x=3$

Then,

$\rm\:3x-1=0$

$\rm\longrightarrow\:3x=0+1$

$\rm\longrightarrow\:3x=1$

$\rm\longrightarrow\:x=\dfrac{1}{3}$

Hence,the required number will be 3 or ⅓.

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✝ Related to quadratic equations :-

Quadratic equations ➝ An equation of the form ax² + bx + c = 0 where a,b,c are real numbers and a ≠ 0 is called an quadratic equations.