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