Math, asked by hechon, 1 year ago

the sum of a number and its reciprocal is 17/4

Answers

Answered by Anonymous
136
x+1/x =17/4
(x²+1)4=17x
4x²-17x+4=0
4x²-16x-x+4=0
4x(x-4)-1(x-4)=0
(4x-1)(x-4)=0
If 4x-1=0
x=1/4
If x-4=0
x=4
Answered by arshikhan8123
0

Concept:

The definition of a quadratic equation as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0

where a, b, and c are numerical coefficients and x is an unknown variable. Here, an is greater than zero because if it equals zero, the equation will cease to be quadratic and change to a linear equation, such as:

bx+c=0

As a result, we cannot refer to this equation as a quadratic equation.

Another name for the terms a, b, and c is quadratic coefficients.

The values of the unknown variable x that fulfil the quadratic equation are the solutions to the problem. These answers are referred to as roots.

Given:

Find:

Solution:

Let x be a number

As per question,

x+1/x =17/4

(x²+1)4=17x

4x²-17x+4=0

4x²-16x-x+4=0

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

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

If 4x-1=0

x=1/4 (rejected, because x is a number)

If x-4=0

x=4

Therefore, the number is 4 and its reciprocal is 1/4

#SPJ3

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