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Three number are in the ratio 1:2:3 . The sum of their cubes is 79092 . Find the numbers
Given: Three numbers are in the ratio $=1:2:3$ and the sum of their cubes$=79092$.
To Find: To find all the three numbers.
Solution:
Let, The first number be $x$.
The second number be $2x$.
The third number be $3x$.
According to the question,
The sum of their cubes is $79092$.
$\Rightarrow x^3+( 2x)^3+( 3x)^3=79092$
$\Rightarrow x^3+8x^3+27x^3=79092$
$\Rightarrow 36x^3=79092$
$\Rightarrow x^3=\frac{79092}{36}$
$\Rightarrow x^3=2197$
$\Rightarrow x=\sqrt[3]{2197}$
$\Rightarrow x=\sqrt[3]{13\times13\times13}$
$\Rightarrow x=13$
Therefore, The first number $=x=1\times13=13$
The second number$=2x=2\times13=26$
The third number$=3x=3\times13=39$
Hence, the three numbers are $13,\ 36$ and $39$.
Updated on: 10-Oct-2022
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