想請問一些國二的數學問題!! 拜託了~~~><?

1.
365 × 363 + 365 × 365 ‒ 364x366 ‒ 364 × 364
= (364 + 1) × (364 ‒ 1) + (364 + 1)² ‒ 364 × (364 + 2) ‒ 364²
= (364² ‒ 1) + (364² + 2 × 364 + 1) ‒ (364² + 2 × 364) ‒ 364²
= 364² ‒ 1 + 364² + 2 × 364 + 1 ‒ 364² + 2 × 364 ‒ 364²
= 0


2.
589 × 591 ‒ 2 × 590 + 2 = K²
K² = 589 × 591 ‒ 2 × 590 + 2
K² = (590 ‒ 1) × (590 + 1) ‒ 2 × 590 + 2
K² = (590² ‒ 1) ‒ 2 × 590 + 2
K² = 590² ‒ 2 × 590 + 1
K² = (590 ‒ 1)²
K² = 589²
K = 589 或 K = ‒589 (不合)

所以 K = 589


3.
2003 × 2005 + 2 × 2004 + 2 = B²
B² = 2003 × 2005 + 2 × 2004 + 2
B² = (2004 ‒ 1) × (2004 + 1) + 2 × 2004 + 2
B² = (2004² ‒ 1) + 2 × 2004 + 2
B² = 2004² + 2 × 2004 + 1
B² = (2004 + 1)²
B² = 2005²
B = 2005 或 B = ‒2005 (不合)

所以 B = 2005


4.
(x + 1)(y ‒ 1)
= x(y ‒ 1) + (y ‒ 1)
= xy ‒ x + y ‒ 1
= (xy ‒ x + y + 6) ‒ 6 ‒ 1
= 0 ‒ 7
= ‒7


5.
[x + (1/y)] [y + (1/x)] = x [y + (1/x)] + (1/y) [y + (1/x)]
6 [y + (1/x)] = xy + 1 + 1 + (1/xy)
6 [y + (1/x)] = [xy + (1/xy)] + 2
6 [y + (1/x)] = 28 + 2
6 [y + (1/x)] = 30
y + (1/x) = 5

4.
(x+1)(y-1)=xy-x+y-1=xy-x+y+6-7=0-7=-7

5.
[x+(1/y)][y+(1/x)]= xy+1+1+(1/xy)=xy+(1/xy)+2
==>(y+(1/x))*6=28+2=30
==>y+(1/x)=5

2.
(590-1)(590+1)-2*590+2=k^2
==>590^2-1-2*590+2=k^2
==>(590-1)^2=k^2
==>589^2=k^2
==>k=589
3.
(2004-1)(2004+1)+2*2004+2=B^2
==>2004^2-1+2*2004+2=B^2
==>(2004+1)^2=B^2
==>2005^2=B^2
==>B=2005

1.
365x363+365x365-364x366-364x364
=(364+1)(364-1)+(364+1)^2-364(366+364)
=364^2-1+364^2+2*364+1-364* 730
=2*364^2+2*364-364*730
=2*364(364+1-365)
=2*364*0
=0

1.設365為x更快

1. 365x363+365x365-364x366-364x364= ?
132495+133225-133224-132496=0


不好意思 我只會一題.希望有幫到你