Question

Find the number of integral solutions of the equation x1x2x3x4 = 210 where x1 x2 x3 x4 are numbers. answer using multinomial theorem

Answer 1

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SOLUTION:--

Answer 2

The number of integral solutions is 2048.

Given:

The equation $x_{1}$ × $x_{2}$ × $x_{3}$ × $x_{4}$ = 210

To Find:

The number of integral solutions of the equation

Solution:

We can solve the problem using the following mathematical process.

Since the prime factorisation of

210 = 2 × 3 × 5 × 7

We have to find out the number of ways we distribute these factors among the four variables $x_{1}$, $x_{2}$, $x_{3}$ and $x_{4}$.

We can distribute each factor among the 4 variables in 4 ways.

Hence, the answer is

$4^{4}$ = 256

Also considering negative numbers, we can multiply the result by = 8

This is because, for negative numbers, only 2 or all 4 variables have to be negative to obtain a positive product.

So, the final answer will be

256 × 8 = 2048

Hence, the number of integral solutions is 2048.

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