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=\(\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
=\(\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
=...=2^32-1
P=2.(5^2-1).(5^2+1).(5^4+1).(5^8+1).(5^16+1)
=2.(5^4-1).(5^4+1).(5^8+1).(5^16+1)
= 2.(5^8-1).(5^8+1).(5^16+1)
= 2.(5^16-1).(5^16+1)
= 2.(5^32-1)
1)P= 12(5^2+1)(5^4+1)(5^8+1)(5^16+1)
=> 2P = 24(5^2+1)(5^4+1)(5^8+1)(5^16+1)
=(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)
=(5^4-1)(5^4+1)(5^8+1)(5^16+1)
=(5^8-1)(5^8+1)(5^16+1)
=(5^16-1)(5^16+1)
=5^32-1
=> P = (5^32-1)/2
a, Với x ≠ 0,x ≠ ± 5 và x ≠ 5/2 thì
P = [x/(x^2 - 25) - (x - 5)/(x^2 + 5x)] : (2x - 5)/(x^2 + 5x) + x/(x - 5)
<=>P = [x/(x - 5)(x + 5) - (x - 5)/x(x+5)] . x(x + 5)/(2x - 5) + x/(x - 5)
=> P = [x^2 - (x - 5)^2]/x(x - 5)(x + 5) . x(x + 5)/(2x - 5) + x/(x - 5)
<=> P = (x - x + 5)(x + x - 5)/(x - 5)(2x - 5) + x/(x - 5)
<=> P = 5(2x - 5)/(x - 5)(2x - 5) + x/(x - 5)
<=> P = 5/(x - 5) + x/(x - 5)
<=> P = (5 + x)/(x - 5)
b, Với x ≠ 0,x ≠ ± 5 và x ≠ 5/2 (x ∈ Z) thì P ∈ Z <=> (5 + x)/(x - 5) ∈ Z
<=> (x - 5 + 10)/(x - 5) ∈ Z
<=> 1 + 10/(x - 5) ∈ Z
<=> 10/(x - 5) ∈ Z
<=> (x - 5) ∈ Ư(10)
<=> x - 5 = 10 <=> x = 15 (TM)
hoặc x - 5 = -10 <=> x = -5 (TM)
hoặc x - 5 = 5 <=> x = 10 (TM)
hoặc x - 5 = -5 <=> x = 0 (TM)
hoặc x - 5 = 2 <=> x = 7 (TM)
hoặc x - 5 = -2 <=> x = 3 (TM)
hoặc x - 5 = -1 <=> x = 4 (TM)
hoặc x - 5 = 1 <=> x = 6 (TM)
Vậy x ∈ {-5,0,3,4,6,7,10,15} thì P ∈ Z
2P = 24.(5^2 + 1 )(5^4 + 1) ... (5^16 + 1)
2P = (5^2 - 1) (5^2 + 1) (5^4 + 1) .. (5^16+1)
2P = (5^4 - 1 )(5^4 + 1 ) (5^8 + 1)
2P = (5^8 - 1 ) (5^8 + 1) (5^16 + 1)
2P = ( 5^ 16 - 1 ) 5^ 16 + 1)
2P = 5^32 - 1
P = (5^32 - 1) : 2
\(P=12.\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(\Rightarrow2P=24\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(\Leftrightarrow2P=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(\Leftrightarrow2P=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(\Leftrightarrow2P=\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(\Leftrightarrow2P=\left(5^{16}-1\right)\left(5^{16}+1\right)\)
\(\Leftrightarrow2P=5^{32}-1\)
\(\Leftrightarrow P=\frac{5^{32}-1}{2}\)
1)a)=>x2+y2+2xy-4(x2-y2-2xy)
=>x2+y2+2xy-4.x2+4y2+8xy
=>-3.x2+5y2+10xy
đặt A=12(5^2+1)(5^4+1)(5^8+1)(5^16+1)
=>2a=24(5^2+1)(5^4-1)(5^8+1)(5^16+1)
=(5^4-1)(5^4+1)(5^8+1)(5^16+1)
=(5^16-1)(5^16+1)
=>A=(5^32-1)/2=1/2(5^32-1)
chúc bạn học toots^..^
thanks