Question

Find a number greater than 1 such that the sum of the number and its reciprocal is 2*4/15.

Answer 1

Dear Student,

Answer: The number is 5/3.

solution:

Let the number is x.

Its reciprocal is 1/x

x+ 1/x = 34/15

$x + \frac{1}{x} =\frac{34}{15} \\ \\ \frac{x^{2}+1}{x} =\frac{34}{15} \\ \\ 15( x^{2} +1) = 34 x\\ \\ 15x^{2} +15 = 34x\\ \\ 15x^{2} -34x+15 =0\\ \\ 15x^{2} -25x-9x+15=0\\ \\ 5x( 3x- 5) -3 ( 3x-5) =0\\ \\ (5x-3) (3x- 5) =0\\ \\ 5x-3 = 0\\ \\ 5x = 3 \\ \\ x= \frac{3}{5} \\ \\ or\\ \\ 3x-5 =0\\ \\ x=\frac{5}{3}$

So that number is 5/3.

( x = 3/5 ; is discarded because it is less than one)

Hope it helps you.

Answer 2

Hi ,

Let us assume the number = a

Reciprocal of the number = 1/a

according to the problem given ,

a + 1/a = 2 4/15

a + 1/a = 34/15

Multiply each term with ' 15a ' , we get

15a² + 15 = 34a

15a² - 34a + 15 = 0

Splitting the middle term ,

15a² - 25a - 9a + 15 = 0

5a( 3a - 5 ) - 3( 3a - 5 ) = 0

( 3a - 5 ) ( 5a - 3 ) = 0

3a - 5 = 0 or 5a - 3 = 0

3a = 5 or 5a = 3

a = 5/3 or a = 3/5

But we require a number greater than 1.

Therefore ,

Required number = a = 5/3

I hope this helps you.

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