✔ 最佳答案
(1)Given the sum of the squares of consecutive integers from 1 to n is S=n(n+1)(2n+1)/6.
a) find 1^2+ 2^2+.......10^2.
=10(10+1)(2乘10+1)/6
=110乘21/6
=385
b)find 1^2+ 2^2+.......20^2.
=20(20+1)(2乘20+1)/6
=420乘41/6
=2870
c)find 11^2+12^2+.......20^2.
=1^2+ 2^2+.......20^2 - ^2+ 2^2+.......10^2.
=2870 - 385
=2485
(2)Make x the subject of each of the following formulae.
1. 2xy+3=2x-y [x]
y+3 = 2x - 2xy
y+3 = x(2 - 2y)
y+3 / 2 - 2y = x
y+3 / 2(1-y) = x
x = y+3 / 2(1-y)
ans:
y+3
x=_____
2(1-y)
3x+1
2.y=____ [x]
1-3x
y(1 - 3x) = 3x+1
y - 3xy = 3x+1
y - 1 = 3x+3xy
y - 1 = 3x(1+y)
y - 1 / 1+y = 3x
y - 1 / 3(1+y) = x
x = y - 1 / 3(1+y)
y-1
x=_____
3(y+1)
2x+3
3.y=____ [x]
x-1
y(x - 1) = 2x+3
xy - y = 2x+3
xy - 2x = y+3
x(y - 2) = y+3
x = y+3 / y - 2
y+3
3.x=___
y-2