Find the value of x satisfying the equation \[ \sqrt{ 3\sqrt{x+5} - \sqrt{x-2} } = 3. \]
Let's neglect negative square roots.
Square both sides so that what we have under the big radical equals 9.
So we've got 3•sqrt(x+5) – sqrt(x–2) = 9
The answer comes out even so each of the sqrts has to come out even.
By a lot of contemplation and a little brute force, I found that x = 11 will work splendidly.
All I did was find a number that would form squares when you add 5 to it and when you subtract 2 from it.
It really wasn't all that hard to do.
Check: 3•sqrt(11+5) – sqrt(11–2) = 3•sqrt(16) – sqrt(9) = 3•4 – 3 = 12 – 3 = 9
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