Question

if a,b,c are three natural numbers a.b.c=27846.if a/6=b+4=c-4 then finf a+b+c.​

Answer 1

Answer:

your answer is 27486/6

Answer 2

Solution:

Given, if a, b, c be three natural numbers,

abc = 27846 ..... (i)

and a/6 = b + 4 = c - 4

Let, a/6 = b + 4 = c - 4 = k (say)

Then, a = 6k, b = k - 4, c = k + 4

From (i), we get

6k (k - 4) (k + 4) = 27846

or, k (k² - 16) = 4641

or, k³ - 16k - 4641 = 0

or, k³ - 17k² + 17k² - 289k + 273k - 4641 = 0

or, k² (k - 17) + 17k (k - 17) + 273 (k - 17) = 0

or, (k - 17) (k² + 17k + 273) = 0

Here k - 17 =0 gives k = 17

and k² + 17k + 273 = 0 gives imaginary solution for k

Therefore, k = 17

Thus, a = 6 * 17 = 102,

b = 17 - 4 = 13 and

c = 17 + 4 = 21

∴ a + b + c = 102 + 13 + 21 = 136