Question 85444
1. Find two consecutive integers such that the sum of there square is 85.
N^2+(N+1)^2=85
N^2+N^2+2N+1=85
2N^2+2N-84=0
N^2+N-42=0
N^2+7N-6N-42=0
N(N+7)-6(N+7)=0
(N-6)(N+7)=0
HENCE N=6 OR -7
THE 2 INTEGERS ARE 6&7
OR -7 AND -6

2. A garden area is 30ft long and 20ft wide. A path of uniform width is set around the edge. If the remaining garden area id 400ft ^2, what is the width of the path?

GARDEN AREA =400 SQ.FT.
IF THE WIDTH OF PATH IS X FEET , THEN 
LENGTH OF GARDEN = 30-X-X=30-2X
WIDTH OF GARDEN =20-X-X=20-2X
AREA OF GARDEN =(30-2X)(20-2X)=400
600-60X-40X+4X^2=400
4X^2-100X+200=0
X^2-25X+50=0

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (25 +- sqrt( 25^2-4*1*50 ))/(2*1) }}}
{{{x = (25+- sqrt( 425 ))/(2) }}}=2.2 FT