Use a direct proof to show that every odd integer is a difference of two squares. (For example: 1 = 12 – 02 and 5 = 32 – 22, and so on.)

We say two numbers m and n are consecutive perfect squares when m is the square of a positive integer a, and n is the square of (a + 1). For example, 4 and 9 are consecutive perfect squares since 4 is the square of 2, and 9 is the square of 3. The year when a man was born and the year when he celebrated his 87th birthday are consecutive perfect squares. In what year was he born? Note: When a man was born, he was 0 years old. When a man celebrated his 87th birthday, he was 87 years old.

Let i denote the square root of -1. Suppose z=12+8i and w=−9−i. Find z(z−w¯). Select one: 308+252i 108+252i 196+252i not in the list 92-132i

= Compute x3 in two ways: by computing x, and x₂, and by computing P³ P= 0.1 0.2 0.9 0.8 x₁ = ₁x₂ = (Simplify your answers.)