I'm guessing
11.
I started by figuring the limits on a.
From the right most radical, 0 <=a <= 5
Then from the next radical, 4 >= √(5 - a)
16 >= (5 - a)
a >= -11, but already a >= 0 not much help.
If you plug a=0 into RHS, you get a (LHS) ≈ 1.328
Iteratively plugging the result back into the RHS for 6 iterations gives 1.4550589
Doing this for all 4 variables gives:
a ≈ 1.4550589332289976
b ≈ 2.370955919705246
c ≈ 1.2266511942949185
d ≈ 2.599364232429259
And then abcd ≈ 10.999989942052382
Which is very close to 11.
So my guess is that it should equal 11
If I call each function once, Product = 11
If I call each function 3 times, Product = 11.000095171765523
If I call each function 6 times, Product = 10.999989942052382
If I call each function 9 times, Product = 10.999999997400211
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def a(x):
return (4 - (5 - x)**.5)**.5
def b(x):
return (4 + (5 - x)**.5)**.5
def c(x):
return (4 - (5 + x)**.5)**.5
def d(x):
return (4 + (5 + x)**.5)**.5
a1 = a(a(a(a(a(a(0))))))
b1 = b(b(b(b(b(b(0))))))
c1 = c(c(c(c(c(c(0))))))
d1 = d(d(d(d(d(d(0))))))
print(a1,b1,c1,d1)
print(a1*b1*c1*d1)
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Posted by Larry
on 2025-03-05 14:41:41 |
Iteration plus guess
