Let α = log10 2, β = log10 3, γ = log10 7. Which of the following choices is closest to an integer?
a) 2β b) 5α + β c) α + 2γ d) 2α + 5β e) 2α + β + γ
Hint: 22 × 35 = 9.72×102
Suppose α, β, γ are roots of the equation:
x3 + 3x2 – 24x + 1 = 0
Find the value of ∛α + ∛β + ∛γ
Suppose a, b, c are real numbers and the following equation is true.
(a + b – 5)2 + (b + 2c + 3)2 + (c + 3a – 10)2 = 0
Find the integer closest to a3 + b3 + c3.
How many integer solutions are there to the system of equations below and which are those solutions?
x^2+y-z = 42 x+y^2-z = 18
Let Ln denote the arc length of the curve x^2n + y^2n = 1 where n is a positive integer. Find Lim (n->∞) Ln
