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Find the only value of x that satisfies: \sqrt{7+\sqrt{5-\sqrt{3+x}}}=3

 Jul 20, 2022
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\( \sqrt{7+\sqrt{5-\sqrt{3+x}}}=3\)

 

Square both sides

 

7  +  sqrt [ 5 - sqrt (3+ x) ]  =  9

 

sqrt  [ 5 - sqrt (3 + x) ]  =  2         square both sides again

 

5 - sqrt (3 + x)  = 4

 

-sqrt (3 + x)  =  -1    square both sides one last time

 

3 + x =   1

 

x =  1  - 3  =    -2

 

 

cool cool cool

 Jul 20, 2022

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