The minimum possible value of the (sum of the) squares of the roots of the equation x² + (a + 3)x − (a + 5) = 0 is

Let f(x) = x² and g(x) = 2x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is

If 9^(x − 1/2) − 2^(2x − 2) = 4^x − 3^(2x − 3), then x is

If x is a real number such that log₃5 = log₅(2 + x), then which of the following is true?

If log(2^a × 3^b × 5^c) is the arithmetic mean of log(2² × 3³ × 5), log(2⁶ × 3 × 5⁷), and log(2 × 3² × 5⁴), then a equals

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

Let a₁, a₂, a₃, a₄, a₅ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a₃. If the sum of the numbers in the new sequence is 450, then a₅ is

Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB, BC, and CA is 4(√2 − 1) cm, then the area, in sq cm, of the triangle ABC is

How many different pairs (a, b) of positive integers are there such that a ≤ b and 1/a + 1/b = 1/9?