# 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

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

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

$$(x-1)(x-2)(x+3)(x+4)+7=x^4+4x^3-7x^2-22x+31$$.

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

$$a^4-a^3+a^2+2=a^4-a^3+2a=a(a^3-a^2+2)=a(a^3+2-2a+2)=a(a(a^2-2)+4)=a(a(2a-4)+4)$$ $$a(a(2a-4)+4)=a(2a^2-4a+4)=2a(a^2+2-2a)=0$$ because $$a^2+2-2a=0$$
Now try to find $$a^4-a^3+a^2+2$$ if $$a^2+a+1=0$$.

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

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

MM

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

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

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

Yeah I also got the solution!!!!!!!

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

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

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

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