Question

if |X| + |Y |= 7 then what is the sum of minimum and maximum value of x + Y

Answer 1

THE MINIMUM VALUE OF x+y WILL BE ATTAINED , WHEN BOTH ARE NEGATIVE
so minimum of x+y = -7

THE MAXIMUM VALUE OF x+y WILL BE ATTAINED , WHEN BOTH ARE POSITIVE
so maximum of x+y = 7

THEN MAX of(x-y) AND MIN of( x+y)= 7+(-7)=0

Answer 2

Minimum value is -7 and maximum value is 7.

Step-by-step explanation:

Given,

|X| + |Y|= 7

By the triangular inequality,

|X + Y| ≤ |X| + |Y|

⇒ |X + Y| ≤ 7,

Since, we know that,

|a| = a if a > 0 and |a| = -a if a < 0,

Thus, there could be two cases,

Case 1 :

X + Y < 0,

⇒  |X + Y| ≤ 7

⇒  -(X+Y) ≤ 7

⇒  X + Y ≥ -7

i.e. minimum value of X + Y is -7.

Case 2:

X + Y > 0,

⇒  |X + Y| ≤ 7

⇒  (X+Y) ≤ 7

⇒  X + Y ≤  7

i.e. maximum value of X + Y is 7.

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