If R (x,y) is a point on the line segment joining the point P ( a ,b) and Q (b ,a) then prove that x + y = a + b .
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Let a be a nonzero rational and let √b be irrational. Then, we have to show that a√b is irrational. ... However, this contradiction arises by assuming that a√b is rational. Hence, a√b is irrational.
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