(1)
75²=5625可写成100×7×(7+1)+25
85²=7225可写成100×8×(8+1)+25
(10n+5)² = 100n(n+1)+25
2005²=(10×200+5)² =100×200×(200+1)+25=4020025
(2)
-2a+3b+8=18
则3b-2a=10
3(3b-2a)=30
得出9b-6a+2=32
(3)
1×3+1=4=2²
2×4+1=9=3²
3×5+1=16=4²
n(n+2)+1=(n+1)²
选A
(4) 解法1:
a+b/a-b=-4
a+b=4b-4a
a/b=3/5
2a+2b/8a-8b=2(a+b)/4(a-b)
由a/b=3/5
根据比例性质得2(a+b)/4(a-b)=2(3+5)/4(3-5)=-2
3(a+b)/a-b = 3(3+5)/(3-5)=-12
a-b/4(a+b) = (3-5)/4(3+5)=-1/16
3(a+b)/a-b 减a-b/4(a+b) =-12-(-1/16)=-191/16
解法二:
设a+b=x; a-b=y;
x/y=-4
2a+2b/8a-8b=2(a+b)/4(a-b)=2x/4y=-2
3(a+b)/a-b = 3x/y=-12
a-b/4(a+b) = y/4x=-1/16
3(a+b)/a-b 减a-b/4(a+b) =-12-(-1/16)=-191/16