The product of two consecutive positive odd numbers is 195. Find the numbers.
Last updated date: 20th Mar 2023
•
Total views: 306.9k
•
Views today: 5.85k
Answer
306.9k+ views
Hint: Assume the numbers as some variables. Frame the equation using the condition given in the question and solve it.
As per the question, let the two positive consecutive odd numbers be $x - 1$ and $x + 1$.
The product of the numbers is given as 196. So, we have:
$ \Rightarrow \left( {x - 1} \right)\left( {x + 1} \right) = 195$
As we know that $\left( {x - a} \right)\left( {x + a} \right) = {x^2} - {a^2}$. Using this formula, we’ll get:
$
\Rightarrow {x^2} - 1 = 195, \\
\Rightarrow {x^2} = 196, \\
\Rightarrow x = \pm \sqrt {196} , \\
\Rightarrow x = \pm 14 \\
$
But we have to consider only positive integers, so we will ignore negative values. $x = 14$ is the valid solution.
$x - 1 = 13{\text{ and }}x + 1 = 15$
Therefore our numbers are 13 and 15.
Note: We can also assume numbers to be $x$ and $x + 2$. In that case, we will get a different quadratic equation but the end result will be the same.
As per the question, let the two positive consecutive odd numbers be $x - 1$ and $x + 1$.
The product of the numbers is given as 196. So, we have:
$ \Rightarrow \left( {x - 1} \right)\left( {x + 1} \right) = 195$
As we know that $\left( {x - a} \right)\left( {x + a} \right) = {x^2} - {a^2}$. Using this formula, we’ll get:
$
\Rightarrow {x^2} - 1 = 195, \\
\Rightarrow {x^2} = 196, \\
\Rightarrow x = \pm \sqrt {196} , \\
\Rightarrow x = \pm 14 \\
$
But we have to consider only positive integers, so we will ignore negative values. $x = 14$ is the valid solution.
$x - 1 = 13{\text{ and }}x + 1 = 15$
Therefore our numbers are 13 and 15.
Note: We can also assume numbers to be $x$ and $x + 2$. In that case, we will get a different quadratic equation but the end result will be the same.
Recently Updated Pages
If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
