a, b, cand dare positive integers, such that a+b+ ab = 76, c+d+ cd = 54. Find (a+b+c+d)·a·b·c·d. Question a, b, cand dare positive integers, such that a+b+ ab = 76, c+d+ cd = 54. Find (a+b+c+d)·a·b·c·d. in progress 0 Math Amelia 4 weeks 2021-12-26T10:37:58+00:00 2021-12-26T10:37:58+00:00 1 Answer 0 views 0

## Answers ( )

Given :a, b, c and d are positive integers, such that a+b+ ab = 76, c+d+ cd = 54To find :(a+b+c+d)·a·b·c·d.Solution:a+b+ ab = 76,

Here a & b are interchangeable

and both has to be even number

if a is odd , b is odd then ab is odd

=> odd + odd + odd = odd while 76 is even

if a is odd & b is even then ab is even

=> odd + even + even = odd

Hence a & b has to be even

a+b+ ab = 76,

=>a (1 + b) = 76 – b

=> a = (76 – b)/(b + 1)

b = 2 => a = 74/3 not possible

b = 4 => a =72/5 not possible

b = 6 => a = 70/7 = 10

( 6 , 10 ) is one solution

b = 8 => a = 68/9 not possible

only Solution

6 , 10

c+d+ cd = 54

Same as above c & d has to be even and interchangeable

c = (54 – d)/(d + 1)

d = 2 => c = 52/3 not possible

d = 4 => c = 50/5 = 10

( 4, 10) is one of the solution

d = 6 => c = 48/7 not possibleand less than 8

Hence only Solution

4 , 10

a + b + c + d = 6 + 10 + 4 + 10 = 30

abcd = 6 * 10 * 4 * 10 = 2400

(a+b+c+d)·a·b·c·d. = 30 * 2400 = 72000

(a+b+c+d)·a·b·c·d. = 72000Learn more:

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