web2.0calc
 
+0  
 

 precalculus 12 question!

0
604
2
avatar

(x+A)^10= 3281250x^4

 

 

 

Find the value of A.

 Feb 24, 2016

2+0 Answers

 #1
avatar
0

Solve for A:
(A+x)^10 = 3281250 x^4

Taking 10^th roots gives 5^(7/10) 42^(1/10) (x^4)^(1/10) times the 10^th roots of unity:
A+x = -(5^(7/10) 42^(1/10) x^(2/5)) or A+x = 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)

Subtract x from both sides:
A = -(5^(7/10) 42^(1/10) x^(2/5))-x or A+x = 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)

Subtract x from both sides:
A = -(5^(7/10) 42^(1/10) x^(2/5))-x or A = 5^(7/10) 42^(1/10) x^(2/5)-x or A+x = -((-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)

Subtract x from both sides:
A = -(5^(7/10) 42^(1/10) x^(2/5))-x or A = 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A+x = (-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)

Subtract x from both sides:
A = -(5^(7/10) 42^(1/10) x^(2/5))-x or A = 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5)-x or A+x = -((-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)

Subtract x from both sides:
A = -(5^(7/10) 42^(1/10) x^(2/5))-x or A = 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A+x = (-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)

Subtract x from both sides:
A = -(5^(7/10) 42^(1/10) x^(2/5))-x or A = 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5)-x or A+x = -((-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)

Subtract x from both sides:
A = -(5^(7/10) 42^(1/10) x^(2/5))-x or A = 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A+x = (-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5) or A+x = -((-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)

Subtract x from both sides:
A = -(5^(7/10) 42^(1/10) x^(2/5))-x or A = 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5)-x or A+x = -((-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)) or A+x = (-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)

Subtract x from both sides:
A = -(5^(7/10) 42^(1/10) x^(2/5))-x or A = 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A+x = (-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)

Subtract x from both sides:
Answer: |  
 | A = -(5^(7/10) 42^(1/10) x^(2/5))-x or A = 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(1/5) 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(2/5) 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(3/5) 5^(7/10) 42^(1/10) x^(2/5)-x or A = -((-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5))-x or A = (-1)^(4/5) 5^(7/10) 42^(1/10) x^(2/5)-x

 Feb 24, 2016
 #2
avatar+118667 
0

 

The only integer solution is A=0 x=0

 

But the curve is shown here.

 

http://www.wolframalpha.com/input/?i=(x%2BA)%5E10%3D+3281250x%5E4

 Feb 24, 2016

2 Online Users

avatar

Top Users

avatar+118667 Melody moderator
avatar+37146 ElectricPavlov
avatar+33657 Alan moderator
avatar+14995 asinus moderator
avatar+9673 MaxWong
avatar+3146 admin administrator
avatar+2653 LiIIiam0216
avatar+2489 GingerAle
avatar+1894 NotThatSmart
avatar+1839 ABJeIIy
avatar+1767 bader

Sticky Topics