SOLUTION: Solve sqrt(x+5)+sqrt(x+10)>=2

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Question 1038727: Solve
sqrt(x+5)+sqrt(x+10)>=2
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve
sqrt(x+5)+sqrt(x+10)>=2
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Square both sides to get::
x+5 + sqrt[(x+5)(x+10)] + x+10 >= 4
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sqrt[x^2+15x+50] >= -2x - 11
sqrt[x^2+15x+50] >= -(2x+11)
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Square both sides to get:
x^2 + 15x + 50 >= 4x^2 + 44x + 121
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3x^2 + 29x + 71 <= 0
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Ans:: no solution
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Cheers,
Stan H.
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Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve
sqrt(x+5)+sqrt(x+10)>=2
~~~~~~~~~~~~~~~~~~~~~~~~~




Figure. Plots y = sqrt%28x%2B5%29%2Bsqrt%28x%2B10%29 and y = 2.

Why not? - They are . . .

Take x = -5. Then

sqrt%28x%2B5%29%2Bsqrt%28x%2B10%29 = sqrt%280%29+%2B+sqrt%285%29 = sqrt%285%29 is just > 2.

Then everything that is greater than -5 satisfies the inequality, too.

Answer. The entire domain {x| x >= -5} is the solution.


Simply there is an error in the previous solution.