I have found some trouble in trying to prove this question.please help mw with that.(adsbygoogle = window.adsbygoogle || []).push({});

Q1) If (a+b)/2 is a rational number can we say that a and b are also rational numbers.? Justify your answer.

I have tried the sum in the following way.

Assume (a+b)/2=p/q (As it is rational)

Lets assume a and b are also rational. Then a=m/n , b=x/y where m,n,x,y ε Z and n,y not equal to 0.

∴ p/q = (my+nx)/2ny = (a+b)/2

∴ (a+b)/2 = m/2n + x/2y

= 1/2(m/n+x/y)

for a and b to be rational they has to be equal to m/n and x/y..That is not the case always so we can't say if (a+b)/2 is rational a and b are also rational.

I doubt that this proof is wrong.Please correct that if there's any wrong.

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# A proof regarding Rational numbers

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