You want to find the value of x that satisfies the inequality:
a^2 + 2ax + x^2 > 0.25ax
First, simplify the expression on the left side of the inequality by factoring it:
(a + x)^2 > 0.25ax
Now, take the square root of both sides to solve for x:
|a + x| > 0.5√(ax)
Now, consider two cases:
If a > 0 and x > 0In this case, the original inequality simplifies toa^2 + 2ax + x^2 > 0.25a(a + x) > 0.5√(ax)
Therefore, the solution is x > 0.5√a.
If a < 0 and x > 0In this case, the original inequality simplifies toa^2 + 2ax + x^2 > 0.25a|a + x| > 0.5√(ax)
Therefore, the solution is x > max(0.5√(-a), -0.5√(-a)).
These are the solutions for x that satisfy the given inequality based on the two possible cases.
You want to find the value of x that satisfies the inequality:
a^2 + 2ax + x^2 > 0.25ax
First, simplify the expression on the left side of the inequality by factoring it:
(a + x)^2 > 0.25ax
Now, take the square root of both sides to solve for x:
|a + x| > 0.5√(ax)
Now, consider two cases:
If a > 0 and x > 0
In this case, the original inequality simplifies to
a^2 + 2ax + x^2 > 0.25a
(a + x) > 0.5√(ax)
Therefore, the solution is x > 0.5√a.
If a < 0 and x > 0
In this case, the original inequality simplifies to
a^2 + 2ax + x^2 > 0.25a
|a + x| > 0.5√(ax)
Therefore, the solution is x > max(0.5√(-a), -0.5√(-a)).
These are the solutions for x that satisfy the given inequality based on the two possible cases.