>> syms a
>> eq=7*a+1/(7*a) == sqrt(98)
eq =
7*a + 1/(7*a) == 7*2^(1/2)
>> sa=solve(eq,a)
sa =
2^(1/2)/2  94^(1/2)/14
2^(1/2)/2 + 94^(1/2)/14
>> eval(sa(1))
ans =
0.0145810872699291
>> eval(sa(2))
ans =
1.39963247510317
>> sa(1)^777
ans =
(2^(1/2)/2  94^(1/2)/14)^777
>> eval(ans)
ans =
0
>> sa(2)^777
ans =
(2^(1/2)/2 + 94^(1/2)/14)^777
>> eval(ans)
ans =
2.83717616726445e+113
saying a = sqrt(2)/2 /+ sqrt(94)/14
Apparently, when the minus sign is used, the 777th power is zero (but don't count on it exactlysee below), but when the plus sign is used, the 777th power is approximately 2.837... x 10^113.
Wolfram Alpha formulates a different form:
a = 7 +/ sqrt(47))/(7 sqrt(2)
but they evaluate to the same approximations.
However, the 777th power of the smaller value is not zero but approximately
1.83975297887821163258528183970279248931825398362582135131... × 10^1427
and the 777th power of the larger value is approximately
2.8371761672641754912015188779177168044380334845625931196230... × 10^113.

Posted by Charlie
on 20230421 10:49:04 