SOLUTION: √(x + 4) > 2 + √x

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Question 1159695: √(x + 4) > 2 + √x
Found 2 solutions by MathLover1, solver91311:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28x+%2B+4%29+%3E+2+%2B+sqrt%28x%29........square both sides

x+%2B+4+%3E+%282+%2B+sqrt%28x%29%29%5E2
x+%2B+4+%3E+4+%2B+4sqrt%28x%29%2Bx
cross%28x%29+%2B+cross%284%29+%3E+cross%284%29+%2B+4sqrt%28x%29%2Bcross%28x%29
0+%3E+4sqrt%28x%29
or
4sqrt%28x%29%3C0 -> since 4%3E0, inequality will be true only if sqrt%28x%29%3C0
=> so, no solution exist because sqrt%28x%29%3E=0 for all real numbers


Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Square both sides:



Add to both sides:



Multiply both sides by



Square both sides



Which is to say:



However, this result must be discarded because the most restrictive domain is the domain of the right-hand side expression, namely



Therefore the solution set is the null set over the reals.


John

My calculator said it, I believe it, that settles it