If (5−√x)2=y−20√2 where x,y are integers, then what are x and y ?
1 Answer
Jun 3, 2015
Expand and equate the irrational parts to help simplify and find:
x=8 andy=33
Explanation:
Expand the left hand side:
(5−√x)2
=52−(2×5×√x)+x
=25−10√x+x
=(x+25)−10√x
In order to eliminate the irrational
−10√x=−20√2
Divide both sides by
√x=2√2
So
x=(2√2)2=8
y=x+25=8+25=33
Footnote
Why is it possible to equate the irrational parts like this?
Consider the set of all numbers of the form
These representations are unique:
Suppose
Then
So if
So we must have