We are required to solve the following system of equations: x^3+1/(3x^4)=5 (1), x^4+1/(3x^3)=10 (2)

Inbrunstlr

Inbrunstlr

Answered question

2022-10-06

We are required to solve the following system of equations:
(1) x 3 + 1 3 x 4 = 5
(2) x 4 + 1 3 x 3 = 10
We may multiply (1) by 3 x 4 throughout and (2) by 3 x 3 throughout (as 0 is not a solution we may cancel the denominators) to yield.
(3) 3 x 7 + 1 = 15 x 4
(4) 3 x 7 + 1 = 30 x 3
Subtracting the two:
15 x 4 30 x 3 = 0
x 3 ( x 2 ) =
As 0 is not a solution we choose x = 2.
But putting x = 2 in the original equations does not satisfy them. How come?

Answer & Explanation

odejicahfc

odejicahfc

Beginner2022-10-07Added 10 answers

Solutions to (3) and (4) are equivalent to solutions of 15 x 4 30 x 3 = 0 and one of (3) or (4). But the solution 15 x 4 30 x 3 = 0 to 15 x 4 30 x 3 = 0 does not satisfy (3) [or equivalently (4)], as 3 2 7 + 1 15 2 4 .
You shouldn't be surprised that a system of two equations in one unknown may be inconsistent, i.e. not have any solutions.

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