Question

For example, the quadratic equation x^2 + 2x + 1 = 0 is a claim concerning some unknown number x.

So if you substitute the x = -1, the claim holds since it would equal 0.
But if you substitute x = 1, the claim won’t be true because you would get 4.

Now I’ve been told to develop a function that tests whether a few problems are in fact a solution.

Where would I start for this one below?

10x – 6 = 7x + 9

Answer 1

It all depends on the chosen representation for functions. If you pass them as lambdas, it’s trivial to test if a “claim” is true or false:

(define (test-claim f1 f2 x)
  (= (f1 x) (f2 x)))

For example:

; x^2 + 2x + 1 = 0, x = -1    
(test-claim (lambda (x) (+ (* x x) (* 2 x) 1))
            (lambda (x) 0)
            -1)

=> #t

; x^2 + 2x + 1 = 0, x = 1    
(test-claim (lambda (x) (+ (* x x) (* 2 x) 1))
            (lambda (x) 0)
            1)

=> #f

; 10x – 6 = 7x + 9, x = 5    
(test-claim (lambda (x) (- (* 10 x) 6))
            (lambda (x) (+ (* 7 x) 9))
            5)

=> #t

; 10x – 6 = 7x + 9, x = 10    
(test-claim (lambda (x) (- (* 10 x) 6))
            (lambda (x) (+ (* 7 x) 9))
            10)

=> #f