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1.Two one by one natural numbers sum 109 is smaller then there product.Find those numbers.
{y=x+1
xy=x+y+109
x=y-1
(y-1)y=x+y+109 Whats next?
2. Right-angled parterres area is 56m2(square),and the fence,that surrounds the parterre is 30m.Find the parterres dimension.
Please someone help.
I'm going to assume you set up the problem correctly because I can't make sense out of the question.Quote:
Originally Posted by Neurok
First you need to replace ALL x's in the second equation:
$\displaystyle xy = x + y + 109$
$\displaystyle (y - 1)y = (y - 1) + y + 109$
$\displaystyle y^2 - y = 2y + 108$
$\displaystyle y^2 - 3y - 108 = 0$
$\displaystyle (y - 12)(y + 9) = 0$
Thus y = 12 or y = -9. This means that x = 11 or x = -10 respectively.
So your solutions are: (x, y) = (11, 12) or (x, y) = (-10, -9).
-Dan
I'm assuming your parterre is a rectangle, rather than a square. So let the dimensions of the parterre be x and y. The we know thatQuote:
Originally Posted by Neurok
$\displaystyle xy = 56$
$\displaystyle 2x + 2y = 30$
From the second equation:
$\displaystyle 2x + 2y = 30$
$\displaystyle x + y = 15$
$\displaystyle y = 15 - x$
Inserting this into the first equation gives:
$\displaystyle xy = 56$
$\displaystyle x(15 - x) = 56$
$\displaystyle 15x - x^2 = 56$
$\displaystyle x^2 - 15x + 56 = 0$
$\displaystyle (x - 7)(x - 8) = 0$
So x = 7 m or x = 8 m. Thus y = 8 m or y = 7 m respectively. Either way the dimensions of the parterre are 7 m by 8 m.
-Dan
Thank you.
