Consider this relationship:
7√x - 5√x = 3√x - √x
Determine the total number of real values of x that satisfy the abovementioned relationship.
syms x
fplot(@(x)x^(1/7)-x^(1/5)-x^(1/3)+x^(1/2))
grid
low=.001; high=.1;y=1;
while low<high && abs(y)>1e-16
mid=(low+high)/2;
x=mid;
y=x^(1/7)-x^(1/5)-x^(1/3)+x^(1/2);
if y<0
high=mid;
else
low=mid;
end
end
x,y
shows that one solution is x=1 and another is very close to zero, and is about x=0.0117154772664753. There is also x=0.
These are the three roots verified by Wolfram Alpha also.
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Posted by Charlie
on 2023-09-01 12:03:55 |
computer solution
