# find max(a+b+c+d)

#### Albert

##### Well-known member
a,b,c,d are integers

given :a+b=c, b+c=d , c+d=a

now if b>0, find max(a+b+c+d)

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##### Well-known member
a,b,c,d are integers

given :a+b=c, b+c=d , c+d=a

now if b>0, find max(a+b+c+d)
by solving we get

a = -3b,
c = -2b
d = -b

so sum = a + b + c + d = - 5b

it is largest when b ls smallest

b = 1 as b > 0 and integer

so largest sum = - 5

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#### chisigma

##### Well-known member
a,b,c,d are integers

given :a+b=c, b+c=d , c+d=a

now if b>0, find max(a+b+c+d)
The linear system of equations...

$$a-c= - b$$

$$c- d= - b$$

$$a - c - d =0\ (1)$$

... has solution $a= - 3 b$, $c=- 2 b$, $d= - b$, so that is $a + b + c + d = - 5 b$ and the maximum is for b= 1, i.e. max (a + b + c + d) = -5...

Kind regards

$\chi$ $\sigma$

P.S. I didn't see that Kaliprasad solved before me... sorry!...