IF X IS a irrational then find x+2
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Step-by-step explanation:
Squaring both sides: But is irrational, while this implies is rational, therefore if is irrational then is rational
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Answered by
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Okay, so we want to prove that
∀x∈ R:(x2∉Q)⇒(x∉Q) .
Using the method of proof by contradiction, let's try to prove that
∃x∈R:(x2∉Q)∧(x∈Q) .
If x is rational, then we can represent it the next way:
x=pq,p∈Z,q∈N .
Let's raise x to the 2nd power:
x2=(pq)2=p2q2 .
But p2 is an integer and q2 is natural:
m=p2∈Z,n=q2∈N .
So we can say that
x2=mn,m∈Z,q∈N,
which means that x2 is rational by definition:
x2∈Q .
This statement contradicts our assumption that x2 is irrational. Therefore, such x doesn't exist.
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