maths

1) Let N be the smaller odd number required. The greater one will be N+2.

We then have N(N+2) = 143
N^2 + 2N -143 =0
(N+13)(N-11)=0
N= -13 or N=11
Checking : if N=-13, N+2 = -11. N(N+2)= (-13)(-11)=143
if N=11, N+2 = 13, N(N+2) = (11)(13) = 143.

The two consecutive odd numbers required ar {-13, -11} or {11, 13}.

2) Let Y be the number of eggs the hen lays

Y(Y-5)= 84
Y^2 -5Y -84=0
(Y-12)(Y+7)=0
Y=12 or Y= -7 (rejected since number of eggs could not be negative).

The number of eggs the hen lays is 12.

1)
Let x be the smaller number
x(x+2)=143
x^2+2x-143=0
x=11 or -13(rej.)
∴The numbers are 11 and 13

2)
x(x+5)=84
x^2+5x-84=0
x=7 or -12(rej.)
∴12eggs

2006-10-17 19:24:15 補充：
第二題因為(x＋5)eggs her hen lays∴所以答案不是7而是7＋5(即是12)

1) 11 x 13 =143

2) sub x=84 into x+5
number of eggs the hen lays = 84+5 =89