What's obvious is that x=0 is a solution, but is it the only solution?
Using Matlab as a calculator:
>> eq=sin(7*x)==7*sin(x)
eq =
sin(7*x) == 7*sin(x)
>> s=solve(eq)
s =
-acos((1/2 - (7^(1/2)*1i)/2)^(1/2)/2)
-acos(((7^(1/2)*1i)/2 + 1/2)^(1/2)/2)
0
acos((1/2 - (7^(1/2)*1i)/2)^(1/2)/2)
acos(((7^(1/2)*1i)/2 + 1/2)^(1/2)/2)
>> for j=1:5
eval(s(j))
end
ans =
-1.09590566854303 - 0.371505531219232i
ans =
-1.09590566854303 + 0.371505531219232i
ans =
0
ans =
1.09590566854303 + 0.371505531219232i
ans =
1.09590566854303 - 0.371505531219232i
>>
shows that there are four other solutions, but they are all complex, so zero is the only real solution.
Without fractional exponents:
-acos(sqrt(1/2 - (sqrt(7)*i)/2)/2)
-acos(sqrt((sqrt(7)*i)/2 + 1/2)/2)
0
acos(sqrt(1/2 - (sqrt(7)*i)/2)/2)
acos(sqrt((sqrt(7)*i)/2 + 1/2)/2)
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Posted by Charlie
on 2023-04-10 10:38:22 |
solution
