Answer
Verified
328.9k+ views
Hint: we need to know the general formula of Arithmetic and Geometric means of two numbers.
It is given that a and b are two numbers.
Arithmetic mean (AM) of the given two numbers is $\frac{{a + b}}{2} = 10$ ... (1)
Geometric Mean (GM) of the given two numbers is $\sqrt {ab} = 8$ ... (2)
On simplifying equation (1) and (2), we get
$ \Rightarrow a + b = 20$ and $ab = 64$
We need to find the unique values of a and b.
Clearly, a and b are roots of the quadratic equation
${x^2} - (a + b)x + ab = 0$
Substituting $\left( {a + b} \right)\&$ ab values
${x^2} - 20x + 64 = 0$
Factorization of the above quadratic equation to find roots
$ \Rightarrow (x - 16)(x - 4) = 0$
$ \Rightarrow x = 4,16$
$\therefore a = 4,b = 16$ or $a = 16,b = 4$ are the required values.
Note: Arithmetic mean is the sum of a collection of all numbers divided by count of numbers in the collection. Geometric mean indicates the central tendency or typical value of a set of numbers by using the product of their values.
It is given that a and b are two numbers.
Arithmetic mean (AM) of the given two numbers is $\frac{{a + b}}{2} = 10$ ... (1)
Geometric Mean (GM) of the given two numbers is $\sqrt {ab} = 8$ ... (2)
On simplifying equation (1) and (2), we get
$ \Rightarrow a + b = 20$ and $ab = 64$
We need to find the unique values of a and b.
Clearly, a and b are roots of the quadratic equation
${x^2} - (a + b)x + ab = 0$
Substituting $\left( {a + b} \right)\&$ ab values
${x^2} - 20x + 64 = 0$
Factorization of the above quadratic equation to find roots
$ \Rightarrow (x - 16)(x - 4) = 0$
$ \Rightarrow x = 4,16$
$\therefore a = 4,b = 16$ or $a = 16,b = 4$ are the required values.
Note: Arithmetic mean is the sum of a collection of all numbers divided by count of numbers in the collection. Geometric mean indicates the central tendency or typical value of a set of numbers by using the product of their values.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Summary of the poem Where the Mind is Without Fear class 8 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Write an application to the principal requesting five class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE