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Find the only value of x that satisfies:

 

 

\(\sqrt{7+\sqrt{4-\sqrt{3+x}}}=3\)

 

 Jul 1, 2020
 #1
avatar+732 
+1

\(\sqrt{7+\sqrt{4-\sqrt{3+x}}}=3\)

\(7+\sqrt{4-\sqrt{3+x}}=9\)     (squared both sides)

\(\sqrt{4-\sqrt{3+x}}=2\)             (subtracted 7 from both sides)

\(4-\sqrt{3+x}=4\)                 (square both sides again)

\(-\sqrt{3+x}=0\)                     (subtracted 4 from both sides)

\(\sqrt{3+x}=0\)                        (divided both sides by -1)

\(3+x=0\)                            (squared both sides again)

\(\boxed{x=-3}\)

 Jul 1, 2020
 #2
avatar+130 
-4

thank you i figured that out! and i got the next simlar question right!

Creampuff  Jul 1, 2020

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