Math, asked by anuragsingh8875, 1 year ago

The sum of a number and it's reciprocal is 17/4.find the number.

Answers

Answered by deepsen640
5

Answer:

The required number = 1

Step-by-step explanation:

given that

The sum of a number and it's reciprocal is 17/4.

let the number be x

so,

it's reciprocal will be 1/x

According to the question,

x + 1/x = 17/4

(x² + 1)/x = 17/4

x² + 1 = 17x/4

x² + 1 - 17x/4 = 0

multiplying the equation by 4

4x² - 17x + 4 = 0

4x² - x - 16x + 4 = 0

4x(x - 1) -4(x - 1) = 0

(4x - 4)(x - 1) = 0

4x - 4 = 0

4x = 4

x = 4/4

x = 1

____________

x - 1 = 0

x = 1

so,

The required number = 1

Answered by ILLIgalAttitude
1

Answer:

The required number = 1

Step-by-step explanation:

let the number be x

ATQ,

x + 1/x = 17/4

(x² + 1)/x = 17/4

x² + 1 = 17x/4

x² + 1 - 17x/4 = 0....(1)

multiply the equation (1) by 4

x²(4) + 1(4) - 17x/4(4) = 0 × 4

4x² - 17x + 4 = 0

4x² - x - 16x + 4 = 0

4x(x - 1) -4(x - 1) = 0

(4x - 4)(x - 1) = 0

4x - 4 = 0

4x = 4

x = 4/4

x = 1

and also,

x - 1 = 0

x = 1

so,

The number is 1

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