Find the value of a^4-a^3+a^2+2 when a^2+2=2a

Find the value of a^4-a^3+a^2+2 when a^2+2=2a

Postby sudarshan » Sat Jun 30, 2012 7:56 am

Find the value of a4-a3+a2+2 when a2+2=2a
ans:0
Factorize
(x-1)(x-2)(x+3)(x+4)+7
sudarshan
 
Posts: 4
Joined: Sat Jun 30, 2012 7:50 am
Reputation: 2

Re: help me

Postby perfectmath » Sat Jun 30, 2012 9:16 am

sudarshan wrote:Find the value of a^4-a^3+a^2+2 when a^2+2=2a
ans:0
Factorize
(x-1)(x-2)(x+3)(x+4)+7

[tex](x-1)(x-2)(x+3)(x+4)+7=x^4+4x^3-7x^2-22x+31[/tex].

User avatar
perfectmath
 
Posts: 25
Joined: Fri Jun 29, 2012 12:21 am
Location: Vietnam
Reputation: 1

Re: Find the value of a^4-a^3+a^2+2 when a^2+2=2a

Postby MM » Sat Jul 07, 2012 9:17 am

[tex]a^4-a^3+a^2+2=a^4-a^3+2a=a(a^3-a^2+2)=a(a^3+2-2a+2)=a(a(a^2-2)+4)=a(a(2a-4)+4)[/tex] [tex]a(a(2a-4)+4)=a(2a^2-4a+4)=2a(a^2+2-2a)=0[/tex] because [tex]a^2+2-2a=0[/tex]
Now try to find [tex]a^4-a^3+a^2+2[/tex] if [tex]a^2+a+1=0[/tex].

User avatar
MM
 
Posts: 82
Joined: Tue Jul 22, 2008 7:36 am
Location: Bulgaria
Reputation: 7

Re: Find the value of a^4-a^3+a^2+2 when a^2+2=2a

Postby sudarshan » Sat Jul 07, 2012 9:39 pm

Thank you MM
If the answer is 0, i have solution.

sudarshan
 
Posts: 4
Joined: Sat Jun 30, 2012 7:50 am
Reputation: 2

Re: Find the value of a^4-a^3+a^2+2 when a^2+2=2a

Postby MM » Sun Jul 08, 2012 1:27 pm

The answer is 0, indeed. Post your solution.

User avatar
MM
 
Posts: 82
Joined: Tue Jul 22, 2008 7:36 am
Location: Bulgaria
Reputation: 7

Re: Find the value of a^4-a^3+a^2+2 when a^2+2=2a

Postby Guest » Wed Jul 18, 2012 9:36 pm

Check this out
a^4-a^3+a^2+2
=a^2(a^2-a+1)+2
=a(-a-a)+2
=a(-2a)+2
=2-2a^3
=2(1-a^3)
=2(1-a)(1+a+a^2)
=2(1-a)(0)
=0
Guest
 

Re: Find the value of a^4-a^3+a^2+2 when a^2+2=2a

Postby sudarshan » Wed Jul 18, 2012 9:38 pm

Guest wrote:Check this out
a^4-a^3+a^2+2
=a^2(a^2-a+1)+2
=a(-a-a)+2
=a(-2a)+2
=2-2a^3
=2(1-a^3)
=2(1-a)(1+a+a^2)
=2(1-a)(0)
=0


It's me. please believe me, i was so exited to post my solution that i forget to log in.

sudarshan
 
Posts: 4
Joined: Sat Jun 30, 2012 7:50 am
Reputation: 2

Re: Find the value of a^4-a^3+a^2+2 when a^2+2=2a

Postby Jessica » Tue Aug 21, 2012 10:16 am

Yeah I also got the solution!!!!!!! :D

Jessica
 
Posts: 12
Joined: Mon Aug 20, 2012 7:31 am
Reputation: 2

Re: Find the value of a^4-a^3+a^2+2 when a^2+2=2a

Postby Guest » Thu Jan 07, 2016 11:55 am

a^4 - a^3 + a^2 + 2 = a^2 (a^2 - a + 1) +2
= a^2 (2a - 2 - a + 1) + 2
= a^2 (a - 1) + 2
= (2a - 2)(a - 1) + 2
= 2 a^2 - 4 a + 4
= 2(a^2 - 2 a + 2)
but a^2 + 2 = 2 a


a^4 - a^3 + a^2 + 2 = 2 (2a - 2a)

= 0
Guest
 

Re: Find the value of a^4-a^3+a^2+2 when a^2+2=2a

Postby Mathmaven53 » Thu Jan 07, 2016 11:58 am

a^4 - a^3 + a^2 + 2 = a^2 (a^2 - a + 1) +2
= a^2 (2a - 2 - a + 1) + 2
= a^2 (a - 1) + 2
= (2a - 2)(a - 1) + 2
= 2 a^2 - 4 a + 4
= 2(a^2 - 2 a + 2)
but a^2 + 2 = 2 a


a^4 - a^3 + a^2 + 2 = 2 (2a - 2a)

= 0

Mathmaven53
 
Posts: 5
Joined: Wed Jan 06, 2016 12:16 pm
Reputation: 6

Re: Find the value of a^4-a^3+a^2+2 when a^2+2=2a

Postby HallsofIvy » Fri Mar 08, 2019 10:35 am

Working "the other way around", if a^2+ 2= 2a then a^2- 2a+ 2= 0. Multiplying by a^2, a^4- 2a^3+ 2a^2= 0.
Then (a^4- 2a^3+ 2a^2)+ (a^3- a^2+ 2)= a^4- a^3+ a^2+ 2= 0+ 0= 0.

HallsofIvy
 
Posts: 145
Joined: Sat Mar 02, 2019 9:45 am
Reputation: 58


Return to Polynomials, Polynomial Identities



Who is online

Users browsing this forum: No registered users and 3 guests