Answer
Verified
412.2k+ views
Hint: We will solve the above question by using the formula \[x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\] . First, we will put the values in the above equation from the given question according to the general quadratic equation. Then, I will find the values of x.
Complete step by step answer:
Let us solve the question.
We have given the equation as \[9{{x}^{2}}-16=0\] .
As we know, the general form of the quadratic equation is \[a{{x}^{2}}+bx+c=0\] .
And the values of x according to the equation \[a{{x}^{2}}+bx+c=0\] are \[\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\] .
According to the above equations, we can say that
a=9, b=0, and c=-16.
Now, we will plug them in the equation \[x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\] , we get
\[x=\dfrac{-0\pm \sqrt{{{0}^{2}}-4\times 9\times (-16)}}{2\times 9}\]
Now, we will simplify the above equation.
\[\Rightarrow x=\dfrac{\pm \sqrt{-4\times 9\times (-16)}}{2\times 9}\]
\[\Rightarrow x=\pm \dfrac{\sqrt{36\times 16}}{18}\]
\[\Rightarrow x=\pm \dfrac{24}{18}\]
\[\Rightarrow x=\pm \dfrac{4}{3}\]
Hence, the values of x are \[\dfrac{4}{3}\] and \[-\dfrac{4}{3}\] .
Note:
In this type of question, we should have a proper knowledge in quadratic equations. We should be careful of the signs. We can solve this by a second method simply. Suppose, we have the equation\[9{{x}^{2}}-16=0\]
We will take the number 16 to the right side of the equation. After that, we will find the value of x.
\[\Rightarrow {{x}^{2}}=\dfrac{16}{9}\]
Now, by taking the square root both sides of the above equation, we get
\[\Rightarrow x=\sqrt{\dfrac{16}{9}}\]
\[\Rightarrow x=\pm \dfrac{4}{3}\]
Therefore, we get the values of x as \[\dfrac{4}{3}\] and \[-\dfrac{4}{3}\].
We have another method of solving the question.
We know that \[{{a}^{2}}-{{b}^{2}}=(a+b)(a-b)\] .
Using this formula, we can find the solution.
Therefore, we can say that \[9{{x}^{2}}-16=(3x+4)(3x-4)\] .
Then, (3x+4)(3x-4)=0
Hence, we can say that \[x=-\dfrac{4}{3}\] and \[x=\dfrac{4}{3}\] .
As we can say that all above methods are giving satisfactory solutions. So, we can use any of the methods to solve them.
Complete step by step answer:
Let us solve the question.
We have given the equation as \[9{{x}^{2}}-16=0\] .
As we know, the general form of the quadratic equation is \[a{{x}^{2}}+bx+c=0\] .
And the values of x according to the equation \[a{{x}^{2}}+bx+c=0\] are \[\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\] .
According to the above equations, we can say that
a=9, b=0, and c=-16.
Now, we will plug them in the equation \[x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\] , we get
\[x=\dfrac{-0\pm \sqrt{{{0}^{2}}-4\times 9\times (-16)}}{2\times 9}\]
Now, we will simplify the above equation.
\[\Rightarrow x=\dfrac{\pm \sqrt{-4\times 9\times (-16)}}{2\times 9}\]
\[\Rightarrow x=\pm \dfrac{\sqrt{36\times 16}}{18}\]
\[\Rightarrow x=\pm \dfrac{24}{18}\]
\[\Rightarrow x=\pm \dfrac{4}{3}\]
Hence, the values of x are \[\dfrac{4}{3}\] and \[-\dfrac{4}{3}\] .
Note:
In this type of question, we should have a proper knowledge in quadratic equations. We should be careful of the signs. We can solve this by a second method simply. Suppose, we have the equation\[9{{x}^{2}}-16=0\]
We will take the number 16 to the right side of the equation. After that, we will find the value of x.
\[\Rightarrow {{x}^{2}}=\dfrac{16}{9}\]
Now, by taking the square root both sides of the above equation, we get
\[\Rightarrow x=\sqrt{\dfrac{16}{9}}\]
\[\Rightarrow x=\pm \dfrac{4}{3}\]
Therefore, we get the values of x as \[\dfrac{4}{3}\] and \[-\dfrac{4}{3}\].
We have another method of solving the question.
We know that \[{{a}^{2}}-{{b}^{2}}=(a+b)(a-b)\] .
Using this formula, we can find the solution.
Therefore, we can say that \[9{{x}^{2}}-16=(3x+4)(3x-4)\] .
Then, (3x+4)(3x-4)=0
Hence, we can say that \[x=-\dfrac{4}{3}\] and \[x=\dfrac{4}{3}\] .
As we can say that all above methods are giving satisfactory solutions. So, we can use any of the methods to solve them.
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
Give 10 examples for herbs , shrubs , climbers , creepers
Change the following sentences into negative and interrogative class 10 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Application to your principal for the character ce class 8 english CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE