729=2x+1/x^4
2^x+3^(x+1)=6
2006-12-31 19:47:21 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
729=2x+1/x^4
729x^4=2x+1
x=-0.173059 or 0.210089
(estimate)
2^x+3^(x+1)=6
x=0.40413
(estimate)
2006-12-31 20:00:30 · answer #1 · answered by josiahitsgoodtohavesomeself-ctrl 2 · 3⤊ 0⤋
For the first question, do you mean (2x + 1)/x^4, or 2x + (1/x^4)?
I'm going to assume you mean the former.
1) 729 = (2x + 1)/(x^4)
Multiply both sides by x^4, to get
729x^4 = 2x + 1
Move everything over to the left hand side,
729x^4 - 2x - 1 = 0
This doesn't have any rational roots. Maybe you meant the other way.
1b) 729 = 2x + (1/(x^4))
Multiply both sides by x^4,
729x^4 = 2x^5 + 1
729x^4 - 2x^5 - 1 = 0
Which, again, does not have rational roots. You may only solve these by approximation.
2) 2^x + 3^(x + 1) = 6
It's not possible to isolate the x to solve this.
In both of your questions, it's not possible to isolate the x; thus, they may only be solved numerically.
2007-01-01 03:56:03 · answer #2 · answered by Puggy 7 · 2⤊ 1⤋
729 = 2x + 1/x^4
729x^4=2x^5 + 1
This equation can be solved by approximation
2^x + 3^(x+1)=6
This equation also can be solved by trial and error method.
2007-01-01 08:04:34 · answer #3 · answered by ATS 2 · 0⤊ 0⤋