SOLUTION: please help me with this problem: One on one: Find two positive real numbers that differ by 1 and have a product of 1. and the next one is Swimming pool design: an architect has de

Question 49662This question is from textbook
: please help me with this problem: One on one: Find two positive real numbers that differ by 1 and have a product of 1. and the next one is Swimming pool design: an architect has designed a motel pool within a rectangular area that is fenced on three sides. If she uses 60 yards of fencing to enclose an area of 352 square yards, then what are the dimensions marked L and W. Assume that L is greater than W. This question is from textbook

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
please help me with this problem: One on one: Find two positive real numbers that differ by 1 and have a product of 1.
LET ONE NUMBER =X...THE OTHER NUMBER IS X-1
THEIR PRODUCT=X(X-1)=1
X^2-X-1=0
X={1+SQRT(1^2+4*1*1)}/2={1+SQRT(5)/2]
HENCE THE 2 NUMBERS ARE {SQRT(5)+1}/2 AND {SQRT(5)-1}/2
and the next one is Swimming pool design: an architect has designed a motel pool within a rectangular area that is fenced on three sides. If she uses 60 yards of fencing to enclose an area of 352 square yards, then what are the dimensions marked L and W. Assume that L is greater than W.
AREA =LW=352
FENCING LENGTH =L+W+L=2L+W=60
W=60-2L
AREA=L(60-2L)=352
60L-2L^2=352
L^2-30L+176=0
(L-22)(L-8)=0
L=22....
W=60-2L=60-44=16
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