2006 iTest Problems/Problem U1
Revision as of 00:36, 1 December 2018 by Rockmanex3 (talk | contribs) (Solution to Problem U1 -- Radical Equation Combo)
Problem
Find the real number 
such that
![\[\sqrt{x-9} + \sqrt{x-6} = \sqrt{x-1}.\]](http://latex.artofproblemsolving.com/e/6/b/e6b65bac4a7c29faa1f80320d9f69fa1767bb77d.png)
Solution
First, square both sides to remove some radicals.
![\[x-9 + 2\sqrt{(x-9)(x-6)} + x-6 = x-1\]](http://latex.artofproblemsolving.com/0/5/4/0549ff507a789d492bdaf64ba4ba5ec686e54f2d.png)
Next, combine terms, isolate the radical part, and square both sides.
Solve for by combining terms into a quadratic.
Because we squared both sides, we have to check for extraneous solutions. Of the two values of , 
does not result in equality while 
does. Thus, the real number that satisfies the equation is 
.
See Also
| 2006 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 40 |
Followed by: Problem U2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • U1 • U2 • U3 • U4 • U5 • U6 • U7 • U8 • U9 • U10 | ||
