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Let a, b, c, and d be distinct real numbers such that
a = \sqrt{4 + \sqrt{5 + a}},
b = \sqrt{4 - \sqrt{7 + b}},
c = \sqrt{4 + \sqrt{9 - c}},
d = \sqrt{4 - \sqrt{11 - d}}.
Compute abcd.
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In the post by @CPhill, the answer produced is 11.
This answer is .
I made a numerical experiment and found the approximate values for
the roots a, b, c and d for each of the four given equations.
Then I found the value of the product of the roots abcd and obtained totally different value as the answer.
The solutions are listed below
equation a = , approx. solution a = 2.59936;
equation b = , approx. solution b = 1.07617;
equation c = , approx. solution c = 2.55701;
equation d = , approx. solution d = 0.90724.
The solutions were found using the online graphical calculator DESMOS at the site
www.desmos.com/calculator.
These solutions were checked, and the checks confirmed their validity.
The product abcd was then calculated and the value was obtained
abcd = 2.59936 * 1.07617 * 2.55701 * 0.90724 = 6.48936. <<<---=== ANSWER
So, the value of abcd CAN NOT be 11,
Thus, the solution by @CPhill is DISPROVED.
The logic in the last part of the "solution" by @CPhill, is
in its last part starting from the words "Let's look for a pattern . . . ".
It only creates the appearance of a logical deducing, but in reality it is a bluff to deceive a reader.
Diagnosis: the "solution" by @CPhill is a TOTAL, GLOBAL and FATAL gibberish.
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Regarding the post by @CPhill . . .
Keep in mind that @CPhill is a pseudonym for the Google artificial intelligence.
The artificial intelligence is like a baby now. It is in the experimental stage
of development and can make mistakes and produce nonsense without any embarrassment.
It has no feeling of shame - it is shameless.
This time, again, it made an error.
Although the @CPhill' solution are copy-paste Google AI solutions, there is one essential difference.
Every time, Google AI makes a note at the end of its solutions that Google AI is experimental
and can make errors/mistakes.
All @CPhill' solutions are copy-paste of Google AI solutions, with one difference:
@PChill never makes this notice and never says that his solutions are copy-past that of Google.
So, he NEVER SAYS TRUTH.
Every time, @CPhill embarrassed to tell the truth.
But I am not embarrassing to tell the truth, as it is my duty at this forum.
And the last my comment.
When you obtain such posts from @CPhill, remember, that NOBODY is responsible for their correctness,
until the specialists and experts will check and confirm their correctness.
Without it, their reliability is ZERO and their creadability is ZERO, too.