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astarmathsandphysics:
http://www.astarmathsandphysics.com/gcse_maths_notes/gcse_maths_notes_completing_the_square.html

sameer210394:

--- Quote from: Tutu_93 on October 17, 2009, 01:18:15 pm ---I have a question in math sl
emm USe the method of completing the square to find the minimum value of y and and x at which it occurs

eg : y=x2 + 4x + 6

Waat do they mean ??

And i have texas Ti-84 silver edition .. how can i use it to graph and that stuff ??

--- End quote ---

one simplest method....

this equation is written in the form of Ax2 + Bx + C

in such cases to find the turning point. use the following equations...

x = -B/2A

then solve for
y(x).

done...

if you want the proving part, plz ask ..

IGSTUDENT:
I have some questions in mathematical induction.

1. let a1,a2,a3,...be a sequence defined by
    a1=1,an=3an-1; n?1

    Show that an=3^n-1 for all positive integers n.


 Prove the following statement.
    n
2. ? 1/(2i-1)(2i+1)=n/2n+1       for each positive integer n.
    1

3. Use mathematical induction to prove that (5^n)+(9^n)+2 is divisible by 4,for n?Z+.

Thanks.

astarmathsandphysics:
. let a1,a2,a3,...be a sequence defined by
    a1=1,an=3an-1; n?1

    Show that an=3^n-1 for all positive integers n.


 Prove the following statement.
    n
2. ? 1/(2i-1)(2i+1)=n/2n+1       for each positive integer n.
    1

3. Use mathematical induction to prove that (5^n)+(9^n)+2 is divisible by 4,for n?Z+.

Thanks.
1.

SO p(1) is true. Suppose p(k) is true, prove p(k+1) trues
Are you sure this question is right?

2.

3.p(1) 5+9+2=16 hence p(1) is true
suppoose p(k) is true then (5^k)+(9^k)+2 is divisible by 4
p(k+1)-p(k) (5^(k+1))+(9^(k+1))+2-(5^k)-(9^n)-2  =5^k(5-1) +9^k(9-1)=4*5^k +8*9^k which is divisible by 4

falafail:

--- Quote from: Tutu_93 on October 17, 2009, 01:18:15 pm ---I have a question in math sl
emm USe the method of completing the square to find the minimum value of y and and x at which it occurs

eg : y=x2 + 4x + 6

Waat do they mean ??

And i have texas Ti-84 silver edition .. how can i use it to graph and that stuff ??

--- End quote ---

y = x2 + 4x + 6
y = x2 + 4x + 22 - 22 + 6
y = (x + 2)2 - 4 + 6
y = (x + 2)2 + 2
the least value of y will be when (x + 2)2 = 0, so x = -2
substitute for y.

so when you're asked to "complete the square" basically this is what you do:
x2 + bx + c
x2 + bx + (b/2)2 - (b/2)2 + c
(x + b/2)2 - (b/2)2 + c
;D

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