Expert: Ahmed Salami - 11/21/2004

Question
Assalumu Alaikum.
I am stuck on the following problems, I would be very grateful if you could help me out. I hope with your help I will be able to tackle the similiar questions in my assignment. Sorry I am unable to represent squared properly with a small two so i'll put an exclaimation mark after them.

1. I need find the roots of:

(x + 1)2!  -  10 = 2x (x - 2)

I know i have to get this in the ax2 + bx + c = 0 format but how?



2. I have no idea how to work out where does the line y=3x cross the curve y2! = x2! + 1/2

I am told it is not done graphically which has confused me further.


finally!
3. A sag "s" metres in a cable streched between two supports, distance "x" metres apart is given by:

S = 35/3x +x

Determine the distance between the two supports when the sag (S) is 35m.


Thankyou very much for taking time to help me.  

Answer
Wa Alaek Salam,
For simplicity, we write the squared of x as x^2.
1)(x+1)^2 = (x + 1)(x + 1)= x^2 + x + x + 1
         = x^2 + 2x + 1
2x(x-2) = 2x^2 - 4x
So,
(x + 1)^2 - 10 = 2x(x - 2) gives
x^2 + 2x + 1 - 10 = 2x^2 - 4x
-9 = x^2 - 2x
x^2 - 2x + 9 = 0
which is now of the format ax^2 + bx + c = 0

2)Every simultaneous equation can be solved graphically and that includes this one.
All we do here is substitute y = 3x into the equation
y^2 = x^2 + 1/2
(3x)^2 = x^2 + 1/2
9x^2 = x^2 + 1/2
8x^2 = 1/2
x^2 = 1/16
x = +or- 1/4
which gives the two values for y as
y = 3(1/4) = 3/4
or
y = 3(-1/4) = -3/4

3)All you have to do here is substitute S = 35 in
S = 35/3x + x
which gives
35 = 35/3x + x
multiplying through by 3x gives
105x = 35 + 3x^2
3x^2 - 105x + 35 = 0
which you can then solve to get the values of S.
I hope it is helpful.
Good luck.
Regards.