Question

22,23 si 24 plsssss repedeee.
Dau coroana!​

Answer 1

22.

2047÷x=c₁ rest 19=> c₁×x+19=2047=>c₁×x=2028

2568÷x=c₂ rest 20=> c₂×x+20=2568=>c₂×x=2548

2101÷x=c₃ rest 21=> c₃×x+21=2101=>c₃×x=2080

2028=2²×13²×3

2548=2²×7²×13

2080=2⁵×5×13

C.M.M.D.C = 2²×13=52

=>x∈D52

=>x∈{1,2,4,13,26,52}

1,2,4 si 13 nu pot avea resturi mai mari decat ele, deci nu pot avea restul 19,20 respectiv 21 => 1,2,4 si 13 nu convin impartirii.

1. 2047÷26=78 rest 19

2568÷26=98 rest 20

2101÷26=80 rest 21

=> x=26

2. 2047÷52=39 rest 19

2568÷26=49 rest 20

2101÷26=40 rest 21

=> x=52

1,2,=> x={26,52}

23.

x÷14=c₁ rest 7

x÷27=c₂ rest 7

x÷42=c₃ rest 7

=>

x=14c₁+7

x=27c₂+7

x=42c₃+7

=>

x-7=14c₁

x-7=27c₂

x-7=42c₃

C.M.M.M.C [14,27,42]

14=2×7

27=3³

42=2×3×7

=> [14,27,42]=2×3³×7=54×7=378

x-7=378

x=385

24.

y÷75=c₁ rest 74

y÷125=c₂ rest 124

y÷180=c₃ rest 179

=>

y=75c₁+74 | +1

y=125c₂+124 | +1

y=180c₃+179 | +1

=>

y+1=75(c₁+1)

y+1=125(c₂+1)

y+1=180(c₃+1)

y+1 ∈ C.M.M.M.C [75,125,180]

75=5²×3

125=5³

180=2²×3²×5

[75,125,180]=5³×3²×2=2250

y+1=2250

y=2249