Determine the exact value of (Square Root of Square Root)

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The discussion revolves around solving the equation x = √(10 + √(10 + √(10 + ...))). The user is trying to determine the exact value of x and has noted a discrepancy between their answer and the textbook's. They suggest forming the equation x² - 10 to find a solution. The conversation emphasizes the need to solve for x using algebraic manipulation. Ultimately, the goal is to clarify the correct value of the infinite nested square root expression.
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Determine the exact value of... (Square Root of Square Root)

I was looking through my textbook and saw a interesting question, I attempted but couldn't get it. (The Answer in Back of Text Book Was Different From Mine..)

Question
Determine the exact value of...

√10+√10+√10...


I tried typing it as well as I can , I uploaded image of question just in case :D

Determine the exact value of:
0sVBk.jpg
 
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Let

x=\sqrt{10+\sqrt{10+\sqrt{10+...}}}

What is

x^2-10

Does this give you an equation that you can solve??
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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