Toán Lớp 6: tìm số nguyên a,b: a^2+ 2a-5 chia hết a-3
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Toán Lớp 6: tìm số nguyên a,b: a^2+ 2a-5 chia hết a-3
Comments ( 2 )
Mà a(a – 3) = a^2 – 3a \vdots a – 3
-> a^2 + 2a – (a^2 – 3a) – 5 \vdots a – 3
-> a^2 + 2a – a^2 + 3a – 5 \vdots a – 3
-> 5a – 5 \vdots a – 3
-> 5a – 15 + 10 \vdots a – 3
-> 5(a – 3) + 10 \vdots a – 3
Mà 5(a – 3) \vdots a – 3
-> 10 \vdots a – 3 (a ∈ ZZ)
-> a – 3 ∈ Ư(10) = { ±1 ; ±2 ; ±5 ; ±10 }
-> a ∈ { 4 ; 2 ; 5 ; 1 ; 8 ; -2 ; 13 ; -7 }