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 #4
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+10
Feb 24, 2016
 #1
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+5
Feb 24, 2016
 #1
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Feb 24, 2016
 #1
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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

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