# Thread: Really hard algebra question help plz

1. ## n>0 and 9xsquared + kx + 36= (3x + n)squared, for all x, what is k-n?

If n>0 and 9xsquared + kx + 36= (3x + n)squared, for all x, what is k-n?

another question i needed to check is this one:
'
A family of five adults and two children are trying to cross a river. They have a lifeboat which can ONLY carry one of the following:
A) One Child
B) Two Children
The boat may not carry two adults or a child and a adult
How many one-way trips for the entire family to cross the river.
How many one-way trips are required for a family of 1000 adults and two children

someone plz answer im a newbie so someone help me plz

2. If 9x^2 + kx + 36 = (3x+n)^2 = (3x)^2 + 2(3x)n + n^2 then equatiing coefficients of x^2, x^1 and x^0 (ie constant term) we have 9=9 (good), k=6n and 36=n^2. So n = +- 6 and given n > 0 we have n=6 and so k=36.

3. 9x^2 +kx +36 = (3x +n)^2
9x^2 +kx +36 = 9x^2 +6n +n^2
Since the lefthand side is equal to the righthand side, then we can say their corresponding terms are equal:
9x^2 = 9x^2 ----(1)
kx = 6n -----(2)
36 = n^2 -----(3)

From (1), x = 1 -------***
From (3), n = sqrt(36) = 6 ---***
So plug those into (2),
kx = 6n
k(1) = 6(6)
k = 36 ------***

Therefore, (k -n) = 36 -6 = 30 -------answer.

=====================
River crossings.

i) 5 Adults and 2 Children, or, 5A and 2C

1st crossing, 2C, ---> across.
2nd crossing, 1C, <--- crossing back.
3rd..., 1A, ---> across. --------------1A already crossed ***
---------------------------
4th..., 1C, <--- crossing back.
5th..., 2C, ---> across.
6th..., 1C, <--- crossing back.
7th..., 1A, ---> across. --------------2A already crossed ***
-------------------------------
8th..., 1C, <--- crossing back.
9th..., 2C, ---> across.
10th..., 1C, <--- crossing back.
11th..., 1A, ---> across. --------------3A already crossed ***
-------------------------------
12th..., 1C, <--- crossing back.
13th..., 2C, ---> across.
14th..., 1C, <--- crossing back.
15th..., 1A, ---> across. --------------4A already crossed ***
-------------------------------
16th..., 1C, <--- crossing back.
17th..., 2C, ---> across.
18th..., 1C, <--- crossing back.
19th..., 1A, ---> across. --------------5A already crossed. 1C is still left at the near side, so the 1C that has crossed will have to go back to fetch the other 1C.
20th..., 1C, <--- crossing back.
21st..., 2C, ---> across. -------------Now, all 5A and 2C are acrossed***

Therefore, for the entire family of 5 adults and 2 children, 21 one-way crossings are required for all of them to cross. -----answer.

==========
ii) For a family of 1000 adults and 2 children?

As seen above where there are 5 adults and 21 crossings were required,
(21 crossings) / (5 adults) = (4 crossings per adult) + (1 extra crossing)