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# **√(x**^{5}+100)·√(x^{3}+100) = 100·x
# Let's solve this equation with **R**:
F = function(x) sqrt(x^5+100)*sqrt(x^3+100)
G = function(x) 100*x
graphF( G, -10,10, "red")
graph ( F, -10,10, "black")
# I zoom in (I get the figure above to the right):
graphF( G, -3,5, 2); graph ( F, -3,5, 1)
# I use solution2 to find when F(x)=G(x)
x1 = more( solution2(F,G, 0,2) )
# [1]** 1.01042408313562**
x2 = more( solution2(F,G, 3,4) )
# [1]** 3.84752572161483**
POINT(x1,F(x1), "green"); POINT(x2,F(x2), "green")
# Alternatively I could study the difference function:
H = function(x) F(x)-G(x)
graphF( H, -3,5, 4)
x1 = more( solution(H,0, 0,2) )
# [1] 1.01042408313562
x2 = more( solution(H,0, 3,4) )
# [1] 3.84752572161483
POINT(x1,H(x1), 2); POINT(x2,H(x2), 2)
If I put:
sqrt(x^5+100)*sqrt(x^3+100) = 100*x
* *
in **WolframAlpha** I get:
The graph is also drawn in intervals that are not part of the function domain (the
program makes simplifications that are valid only in the complex number environment).
In subsequent outputs this is specified, but it is not easy to interpret what is
written.
* *
If I put:
solve sqrt(x^5+100)*sqrt(x^3+100)=100*x for x
* *
I also get this solution x=-5.4596… which corresponds to the red ball on the left
I have to put:
* *
solve sqrt(x^5+100)*sqrt(x^3+100)=100*x** for x real**
* *
to have only the two solutions, which I can then display with more digits:
* *
1.0104240831356162305727839406877928101586173…
3.8475257216148307302699208237021743743216426…