Exercise 1.3

The Question

Define a procedure that takes three numbers as arguments and returns the sum of the squares of the two larger numbers.

The Answer

Prerequisites

Since we need to square twice, we'll first define the procedure square

(define (square x)
  (* x x))

(square 7)
49

As well as max to find the max of two numbers:

(define (max a b)
  (if (> a b) a b))

Testing max:

(max 1 2)
2

(max 2 1)
2

Final solution

To define the procedure we must first find the 2 largest numbers. Then we individually square them, and sum the squares.

Let's call the 3 numbers a, b and c. We can only compare a pair with max, but if we call max twice repeating b, we can establish a relationship between all 3 numbers and compare them. Since we call max twice, we also get 2 results, which are the 2 largest numbers.

Thus, we can use square and max to define the required procedure which we'll call answer:

(define (answer a b c)
  (+ (square (max a b)) (square (max b c))))

(answer 1 2 3)

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