Question 1209775
.
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  {{{highlight(highlight(INCORRECT))}}}.


        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.



<pre>
The solutions are listed below


    equation  a = {{{sqrt(4+sqrt(5+a))}}},   approx. solution  a = 2.59936;

    equation  b = {{{sqrt(4-sqrt(7+b))}}},   approx. solution  b = 1.07617;

    equation  c = {{{sqrt(4+sqrt(9+c))}}},   approx. solution  c = 2.55701;

    equation  d = {{{sqrt(4-sqrt(11-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.    <<<---=== <U>ANSWER</U>



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 {{{highlight(highlight(TOTALLY))}}} {{{highlight(highlight(INVALID))}}}
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.
</pre>

<H3>Diagnosis: the "solution" by @CPhill is a TOTAL, GLOBAL and FATAL gibberish.</H3>


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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;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.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It has no feeling of shame - it is shameless.



This time, again, &nbsp;it made an error.



Although the @CPhill' solution are copy-paste &nbsp;Google &nbsp;AI solutions, &nbsp;there is one essential difference.


Every time, &nbsp;Google &nbsp;AI &nbsp;makes a note at the end of its solutions that &nbsp;Google &nbsp;AI &nbsp;is experimental
and can make errors/mistakes.


All @CPhill' solutions are copy-paste of &nbsp;Google &nbsp;AI &nbsp;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, &nbsp;@CPhill embarrassed to tell the truth.

But I am not embarrassing to tell the truth, &nbsp;as it is my duty at this forum.



And the last my comment.


When you obtain such posts from @CPhill, &nbsp;remember, &nbsp;that &nbsp;NOBODY &nbsp;is responsible for their correctness, 
until the specialists and experts will check and confirm their correctness.


Without it, &nbsp;their reliability is &nbsp;ZERO and their creadability is &nbsp;ZERO, &nbsp;too.