Is solution ok?

Quote:

Originally Posted by DenMac21

I have to solve this irrational inequality:
$\sqrt {25 - x^2 } + \sqrt {x^2 + 7x} > 3$

Is this solution?

Hello,

the bad news first: The right solution is: $x \in \{0 \leq x \leq 5\}$

The first root is defined for $x \in \{-5 \leq x \leq 5\}$

the second root is defined for $x \in \{x \leq -7 \vee x \geq 0\}$

that means the LHS of your inequality is defined for $x \in \{0 \leq x \leq 5\}$

For all x from 0 to 4 the first root is greater than 3, that means the inequality is true for $x \in \{0 \leq x \leq 4\}$

For all x greater than 4 the second root alone has a value greater than $\sqrt{44} \approx 6.6$

Therefore the inequality is true for all $x \in \{0 \leq x \leq 5\}$

Best wishes

Bye