Dear Sir/Madam,

Could you answer this problem as soon as possible please?

For what values of a is the distance between P(a, 3) and Q(5, 2a) greater than the square root of 26.


Use the distance function find the distance between P and Q, that is

Hence you want to find all values of a such that

Since the quantities under each root are positive this is equivalent to solving

Add -26 to both sides, expand the left side and simplify. You then have an inequality to solve with a quadratic on the left and zero on the right. You may find it easier to first replace the inequality by an equality and solve.

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