Question

Find two consecutive multiples of \[3\] whose product is \[270\].

Answer 1

Hint: We have to find the value of the numbers such that they are two consecutive multiples of \[3\] and which then multiplied with each other gives us \[270\] as a product. We solve this question using the concept of solving a polynomial equation. We should have the knowledge of how to split an equation into its roots. We should also know about the concept of consecutive terms. We first consider the numbers to be a variable and then we obtain an equation by multiplying the terms of the expression and then equating it to the value of the product. Then on solving the equation, we will obtain the value of the two numbers.

Complete step by step answer:
Given:
Two consecutive multiple of \[3\] whose product is \[270\]
Let us consider the two numbers to be \[x\] and \[x + 3\] .
So , according to the given condition , we can write the expression as :
\[x\left( {x + 3} \right) = 270\]
Now, we can expand the expression as:
\[{x^2} + 3x = 270\]
On further simplifying, we can write the expression as:
\[{x^2} + 3x - 270 = 0\]
Now splitting the equation, we can write the expression as:
\[{x^2} + 18x - 15x - 270 = 0\]
On taking the terms common, we can write the expression as:
\[x\left( {x + 18} \right) - 15\left( {x + 18} \right) = 0\]
Further simplifying, we can write the expression as:
\[\left( {x + 18} \right)\left( {x - 15} \right) = 0\]
Hence, we get the value for \[x\] as:
\[x = 15\] or \[x = - 18\]
Neglecting the negative value, we get the value of \[x\] as:
\[x = 15\]
Also, we get the value of the other number as:
\[x + 3 = 15 + 3\]
\[x + 3 = 18\]

Hence, the two consecutive multiples of \[3\] whose product is \[270\] are \[15\] and \[18\].

Note:
We neglected the negative value as of \[x\] as the value of the product is positive. We will obtain the value of the product as \[270\], if we use the negative value but we generally neglect the negative value in such questions involving the age, product of terms, value of the numerator etc .