Question

Show that (7+√7)(7-√7) is a rational number

Answer 1

as there is an identity used (a +b ) (a- b) =a^2 -b^2
(7)^2-( root7)^2
= 49-7
=42
42 is a rational no.

Answer 2

Use the difference of two squares which is a^2 - b^2 = (a-b) (a+b)

Therefore it is 7^2 - (root 7)^2 which is 49 - 7 = 42.

And 42 is a rational number.

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