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APRIL [3]
[Last up-dated  03/04/08]
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Thursday

APRIL

3

4:00-5:00 p.m.
Finding two numbers a and b
knowing the Sum and the Product
a + b = S
a.b = P
In this case a and b are the solutions of the equation :
X2 - SX + P = 0
Conditions  for 2 solutions : S2 - 4P > 0
Conditions  for 1 solutions : S2 - 4P = 0
Specific case :
S = P = 4
S = P = y : S2 - 4P = S2 - 4S = S(S-4)
therefore there will be only one double solution
if and only if y = 4 , then a = b = 2,
or y = 0 , then a = b = 0.

Geometric interpretation :
  1. Of all  rectangles of same area a.b = P, the one which has the smallest perimeter is the square (a=b).
    because the smallest possible value of  S  is such that S2 = 4P, and in this case a = b.
  2. Of all rectangles of same perimetera + b  = S, the one which has the greatest area is the square (a=b).
    because the greatest possible value of  P  is such that 4P = S2, and in this case a = b.


 SM6


rectab
Sheet # 4
Thursday
APRIL
10
4:00-5:00 p.m.

Cours avec M. PILVEN
Thursday
APRIL
17
4:00-5:00 p.m.
Cours avec M. PILVEN