Math, asked by sruthiraj22019, 8 months ago

A number when added to its
reciprocal, the result becomes
double of the number, then the
number is​

Answers

Answered by ishwarsinghdhaliwal
3

Answer:

±1

Step-by-step explanation:

Let the required number be x

According to the question

x +  \frac{1}{x}  = 2x \\   \frac{ {x}^{2} + 1 }{x}  = 2x \\  {x}^{2}  + 1  =  2 {x}^{2}  \\ 2 {x}^{2}  -  {x}^{2}  - 1 = 0 \\  {x}^{2}  - 1 = 0 \\  {x}^{2}  = 1 \\ x =  ±1

Answered by GraceS
12

Given :

A number when added to its

reciprocal, the result becomes

double of the number

To find :

The number.

Solution :

Let the number be x

According to question

 \tt\:⟶ x +  \frac{1}{x}  = 2x \\

 \tt\:⟶ \frac{ {x}^{2} + 1 }{x}  = 2x \\

  • Multiplying x on both sides

 \tt\:⟶ \frac{ {x}^{2} + 1 }{x}  \times x = 2x \times x \\

\tt\:⟶ \frac{ {x}^{2} + 1 }{ \cancel x}  \times \cancel x = 2x \times x \\

\tt\:⟶  {x}^{2} + 1  = 2x {}^{2}

\tt\:⟶2 {x}^{2}  -  {x}^{2}  - 1 = 0

\tt\:⟶ {x}^{2}  - 1 = 0

\tt\:⟶ {x}^{2}   =  1

\tt\:⟶ {x}   = ±1

Hence, the number is ±1 i.e. 1 or -1.

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