Question

let p,q, r, s be the positive rationals such that p+✓q=r+✓s then either p=r and q=s or b and d are squares of rationals​

Answer 1

Step-by-step explanation:

If a=c, then a+b=c+d⇒b=d⇒b=d

So, let a=c. Then, there exists a positive rational number x such that a=c+x.

Now,

⇒a+b=c+d

⇒c+x+b=c+d [∵a=c+x]

⇒x+b=d

⇒(x+b)2=(d)2

⇒x2+2bx+b=d

⇒b=2xd−x2−b

hope it helps uh!

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