Answer
Verified
411.3k+ views
Hint: let the number be so its reciprocal will become and by putting these values in the original equation. We will get a quadratic equation and then by solving the equation we will get our required answer.]
Step by step solution:
Let the number be \[x\].
So its reciprocal will be become \[\dfrac{1}{x}\]
And as per the question \[x + \dfrac{1}{x} = \dfrac{{17}}{4}\]
Now, we will try to form a quadratic equation
\[\begin{array}{l}
\Rightarrow \dfrac{{{x^2} + 1}}{x} = \dfrac{{17}}{4}\\
\Rightarrow 4{x^2} - 17x + 4 = 0
\end{array}\]
So, we get our quadratic equation. Now, we will try to find the value of x by factoring it
\[4{x^2} - 16x - x + 4 = 0\]
Taking \[4x\] common from the first part and \[ - 1\] common from the second part.
\[\begin{array}{l}
\Rightarrow 4x\left( {x - 4} \right) - 1\left( {x - 4} \right) = 0\\
\Rightarrow \left( {4x - 1} \right)\left( {x - 4} \right) = 0
\end{array}\]
Now, by comparing the value we will get the values of x
\[x = \dfrac{1}{4},x = 4\]
So, our required answer is \[x = \dfrac{1}{4},x = 4\]
Note:
While letting the number in this type of question we need to take care that the value of x should not be zero otherwise we will get the value of \[\dfrac{1}{x}{\rm{ }}as{\rm{ }}\dfrac{1}{0}\] or \[\infty \] and also while finding the roots we must consider both the values that is \[ + \]as well as \[ - \]. For finding the roots we can also find one formula which is known as the sridharacharya formula in which we get both the roots of the equation. We can also find the quadratic equations if the roots are given . In that case we only need a sum of roots as well as a product of roots.
Step by step solution:
Let the number be \[x\].
So its reciprocal will be become \[\dfrac{1}{x}\]
And as per the question \[x + \dfrac{1}{x} = \dfrac{{17}}{4}\]
Now, we will try to form a quadratic equation
\[\begin{array}{l}
\Rightarrow \dfrac{{{x^2} + 1}}{x} = \dfrac{{17}}{4}\\
\Rightarrow 4{x^2} - 17x + 4 = 0
\end{array}\]
So, we get our quadratic equation. Now, we will try to find the value of x by factoring it
\[4{x^2} - 16x - x + 4 = 0\]
Taking \[4x\] common from the first part and \[ - 1\] common from the second part.
\[\begin{array}{l}
\Rightarrow 4x\left( {x - 4} \right) - 1\left( {x - 4} \right) = 0\\
\Rightarrow \left( {4x - 1} \right)\left( {x - 4} \right) = 0
\end{array}\]
Now, by comparing the value we will get the values of x
\[x = \dfrac{1}{4},x = 4\]
So, our required answer is \[x = \dfrac{1}{4},x = 4\]
Note:
While letting the number in this type of question we need to take care that the value of x should not be zero otherwise we will get the value of \[\dfrac{1}{x}{\rm{ }}as{\rm{ }}\dfrac{1}{0}\] or \[\infty \] and also while finding the roots we must consider both the values that is \[ + \]as well as \[ - \]. For finding the roots we can also find one formula which is known as the sridharacharya formula in which we get both the roots of the equation. We can also find the quadratic equations if the roots are given . In that case we only need a sum of roots as well as a product of roots.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE