Courses
Courses for Kids
Free study material
Free LIVE classes
More
LIVE
Join Vedantu’s FREE Mastercalss

The sum of the squares of two consecutive odd numbers are 394. Find the product of two
numbers.

Answer
VerifiedVerified
366.3k+ views
Hint:- The odd consecutive numbers has a difference of two.

\[ \Rightarrow \]Let two consecutive odd numbers be \[x\] and \[x + 2\]
So, according to the given condition in question
\[ \Rightarrow {x^2} + {\left( {x + 2} \right)^2} = 394\] (1)
Now, for solving equation 1. We get,
\[
   \Rightarrow {x^2} + {x^2} + 4x + 4 = 394 \\
   \Rightarrow 2{x^2} + 4x + 4 = 394 \\
\]
Solving above equation. We get,
\[ \Rightarrow {x^2} + 2x - 195 = 0\]
Now, for solving above equation we split 2x, it becomes
\[ \Rightarrow {x^2} + 15x - 13x - 195 = 0\]
Taking common factors of the above equation to get the value of \[x\].
\[
   \Rightarrow x\left( {x + 15} \right) - 13\left( {x + 15} \right) = 0 \\
   \Rightarrow \left( {x + 15} \right)\left( {x - 13} \right) = 0 \\
\]
Hence possible values of \[x\] are -15 and 13.
But x cannot be negative.
\[ \Rightarrow So,{\text{ }}x = 13\]
\[ \Rightarrow \]So, the first odd number will be 13.
\[ \Rightarrow \]And, another odd number will be \[13 + 2 = 15\].
So, we have two find the product of these two odd numbers.
\[ \Rightarrow \]Required product\[ = 13*15 = 195\].
Hence, the product of two consecutive numbers whose sum of squares is 394 is 195.

Note:- Whenever we come up with this type of problem then first assume two numbers such that they depend on each other (to make calculations easy) like here we assume x+2 which depends on x. And then find the value of the variable using the given condition. Then we should multiply two numbers to get the required answer.
Last updated date: 01st Oct 2023
Total views: 366.3k
Views today: 9.66k