can anyone tell me how to prove a sum of rational and irrational is equal to irrational number
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Answer:
The proof is given below↓
Step-by-step explanation:
First 'a/b' be any rational number. 'x' be any irrational number.
To prove :- a/b + x = irrational
Assume that a/b + x is rational.
a/b + x = m/n (where m/n is a rational number)
x = m/n - a/b
Take LCM =
'nb' is an integer which is rational.
'mb' is an integer which is rational.
'an' is an integer which is rational.
∴ we can conclude that 'x' = rational.
But we took 'x' as irrational.
It was our contradiction.
∴ Our assumption was wrong and 'x' is an irrational number.
Hence proved !
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