Question

The difference of a number and its reciprocal is 15/4 find the number.​

Answer 1

15/4-its reciprocal

=15/4-4/15

225/60

=3 29/60

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Answer 2

Answer:

Required number is 4 or (-1/4)

Step-by-step explanation:

Given,the difference of a number and its reciprocal is 15/4.

Let the number be x.

Now reciprocal of x is $\frac{1}{x}$

According to question,

$x - \frac{1}{x} = \frac{15}{4} \\ \frac{ {x}^{2} - 1}{x} = \frac{15}{4} \\ 4 {x}^{2} - 4 = 15x \\ 4 {x}^{2} - 15x - 4 = 0 \\ 4 {x}^{2} - (16 - 1)x - 4 = 0 \\ 4{x}^{2} - 16x + x - 4 = 0 \\ 4x(x - 4) + (x - 4) = 0 \\ (x - 4)(4x - 1) = 0 \\ (x - 4) = 0 \: or \: (4x + 1) = 0 \\ x = 4 \: or \: - \frac{1}{4}$

So, required number is 4 or (-1/4)

This is a problem of Equation part of Algebra.

Some important Algebra formulas.

(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)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549

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