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