Lời giải:
Bạn áp dụng công thức $(a-b)(a+b)=a^2-b^2$
$15(2^4+1)(2^8+1)(2^{16}+1)=(2^4-1)(2^4+1)(2^8+1)(2^{16}+1)$
$=(2^8-1)(2^8+1)(2^{16}+1)=(2^{16}-1)(2^{16}+1)=2^{32}-1$
a, \(M=1+9^{100}+94^{100}+1994^{100}\)có phải số chính phương không?
b, CMR: \(20^{15}-1⋮11\)
c, CMR: \(2^{30}+3^{30}⋮13\)
d,CMR: \(2^{28}-1⋮29\)
tìm GTNN:
A= \(x^2-4xy+5y+10x-2zy+28\)
B= \(\left(x-1\right)\left(x-2\right)\left(x-3\right)\left(x-4\right)+15\)
a, A= (\(\dfrac{1}{3}\)-1)*(\(\dfrac{1}{6}\)-1)*(\(\dfrac{1}{10}\)-1)*(\(\dfrac{1}{15}\)-1)*(\(\dfrac{1}{21}\)-1)*(\(\dfrac{1}{28}\)-1)*(\(\dfrac{1}{36}\)-1)
b, B= (\(\dfrac{6}{8}\)+1)*(\(\dfrac{6}{18}\)+1)*(\(\dfrac{6}{30}\)+1)*...*(\(\dfrac{6}{10700}\)+1)
4)Tính nhanh
a) 34^2 + 66^2 + 68 . 66 ( . là đấu nhân )
b 74^2 + 24^2 - 48 . 74 ( . là đấu nhân )
c) 729^2 - 728^2
d) 1001^2 - 1
5)Rút gọn
a) ( 2 + 1 )( 2^2 + 1 )( 2^4 + 1 )( 2^8 + 1 )
b) 7 ( 2 ^3 + 1 )( 2^6 + 1 )( 2^12 + 1 )( 2^24 + 1 )
c) ( x^2 - x + 1 ) ( x^2 + x + 1 ) ( x^2 + 1)
(x2 + x + 1)*(x3 + 1)*(x6 + 1)*(x12 + 1)*(x24 + 1), biết x=2
Tìm x biết
\(\dfrac{x.\left(x-1\right)}{2}=28\)
PHƯƠNG PHÁP THÊM BỚT HẠNH TỬ VÀ PHƯƠNG PHÁP ĐỔI BIẾN :
a) \(4x^4+1\)
b) \(x^8+4\)
c) \(x^4+x^2+1\)
d) \(x^7+x^5+1\)
e) \(x^7+x^5-1\)
f) \(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16\)
g) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
h) \(\left(x-1\right)\left(x-3\right)\left(x-5\right)\left(x-7\right)-20\)
i) \(\left(x-1\right)\left(x+2\right)\left(x+3\right)\left(x+6\right)-28\)
PHÂN TÍCH:
a)\(\left(x^2+8x+12\right)\left(x^2+12x+32\right)+16\)
b)\(\left(x^2+6x+8\right)\left(x^2+8x+15\right)-24\)
c)\(\left(x^2-6x+5\right)\left(x^2-10x+21\right)-20\)
d)\(\left(x^2+x-2\right)\left(x^2+9x+18\right)-28\)
e)\(\left(x^2-11x+28\right)\left(x^2-7x+10\right)-72\)
f) \(\left(x^2+5x+6\right)\left(x^2-15x+56\right)-144\)
g)\(\left(x^2-x\right)^2+3\left(x^2-x\right)+2\)
h)\(\left(x^2+5x\right)^2+10x^2+50x+24\)
i)\(x^4+2016x^2+2015x+2016\)
