Toán Lớp 9: Cho P=(√x+3):(√x+1),tìm x nguyên để P nguyên dương
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Toán Lớp 9: Cho P=(√x+3):(√x+1),tìm x nguyên để P nguyên dương
Comments ( 2 )
Ta có : P={\sqrt{x}+3}/{\sqrt{x}+1}
P={\sqrt{x}+1+2}/{\sqrt{x}+1}
P={\sqrt{x}+1}/{\sqrt{x}+1}+2/{\sqrt{x}+1}
P=1+2/{\sqrt{x}+1}
P in Z khi \sqrt{x} + 1 in Ư(2)
<=>\sqrt{x}+1 in {+-2;+-1}
=> P nguyên dương khi \sqrt{x}+1 in {2;1} (Vì 2>0)
Với \sqrt{x}+1=2=>\sqrt{x}=1=>x=1(t//m)
Với \sqrt{x}+1=1=>\sqrt{x}=0=>x=0(t//m)
Vậy x in {1;0} để P nguyên dương