Question

sa se determine x natural si n natural nenul
stiind ca x+|x-4|+2^n=36
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Answer 1

x + | x - 4 | + 2^n = 36

2^n < 36 -> 2^n < 2^5 < 36

Deci n € { 1 , 2 , 3 , 4 , 5}

Cazul n = 1

x + | x - 4 | = 34

cum x>0 -> 2x = 34 + 4 -> x = 19

Cazul n = 2

x + | x - 4 | = 32

2x = 32 + 4 -> x = 18

Cazul n = 3

x + | x - 4 | = 28

2x = 32 , x = 16

Cazul n = 4

x + | x - 4 | = 20

2x = 20 + 4 , x = 12

Cazul n = 5

x + | x - 4 | = 4

1) x + x - 4 = 4

2x = 8 , x = 4

| x - 4 | > 0 -> x € { 0 , 1 , 2 , 3 , 4 , 5 , 6 ...}

x = 0 ,

0 + | 0 - 4 | + 32 = 36

0 + 4 + 32 = 36 A.

x = 1

1 + | 1 - 4 | + 32 = 36

4 + 32 = 36 A.

x = 2 , x = 3 ( amandoua dau solutia Adevarat)

Soluții: { ( 19 , 1) ; ( 18 , 2) ; (16 , 3) ; (12 , 4) ; ( 1 , 5) ; ( 0 , 5) ; ( 2 , 5) ; ( 3 , 5) ; (4 , 5)}