Math, asked by hollo3521, 1 year ago

Prove that 7-√3 is an irrational

Answers

Answered by LAKSHMINEW
1

HERE IS UR ANSWER FRIEND:-

7-ROOT3 IS AN IRRATIONAL AS IT IS NOT IN THE FORM P BY Q.

HOPE IT HELPED U FRIEND!!✌✌

Answered by fanbruhh
16

\huge \bf \red{ \mid{ \overline{ \underline{ANSWER}}} \mid}

Let 7-√3 be a rational number

hence

\bf{7 - \sqrt{3} = \frac{p}{q} }

where p and q are integers and q≠0

\bf{ \implies \: \sqrt{3} = \frac{p}{q} - 7}

\bf{ \implies \: \sqrt{3} = \frac{p - 7q}{q}}

Here ,

\begin{lgathered}\bf{ \frac{p - 7q}{q} is \: rational} \\ \\ \bf{but \: \sqrt{3} is \: irrational} \\ \\ \bf{hence \: the \: contradiction \: we \: } \\ \\ \bf{supposed \: is \: wrong}\end{lgathered}

\begin{lgathered}\huge \mathfrak{hence} \\ \\ \huge \mathfrak{ \sqrt{3} \: is \: irrational}\end{lgathered}

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