Quote:
Originally Posted by sashi
can someone help me and explain how to solve this? i hope somene can solve this and help me XD
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Look at the left hand side (LHS) of the inequality. For what values of x does the LHS become less than 0? 1 sqrt(3) is approx. 0.73205.
x  0.73205 <= 0
x <= 0.73205
So for those values of x, is the right hand side (RHS) ever less than 0?
10(0.73205)^2 + 7 = 12.359
As x gets smaller than 0.73205, the RHS is never less than zero. So all values of x <= 0.73205 satisfy the inequality.
Now we need to check values of x greater than 0.73205
The LHS is the graph of a line, while the RHS is a parabola opening upward with a vertex at (0,7). So for values of x >0.73205 the parabola will always be greater than the line since it increases at a faster rate than the line.
Therefore, all real values of x will satisfy the inequality. If x can be a complex number, then the solution is more difficult.