Math, asked by girishkumar63854, 6 months ago

IF X IS a irrational then find x+2

Answers

Answered by banwarilalgupta758

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 Anonymous

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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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