Question

find 1\x with rational denominator if x=√5+2​

Answer 1

1/x=1/√5+2

1/√5+2×√5-2/√5-2

√5-2

hence we got the answer

Answer 2

Answer:

The solution is √5 - 2.

Step-by-step explanation:

To find : $\frac{1}{x}$

Given : x = √5+2

Concept: In order to rationalize the denominator, we must multiply the the numerator and denominator with the rationalizing factor of the denominator. Rationalizing factor is multiplied with an irrational number to convert the number to a rational number.

Solution :

Step I : Put the value of x in $\frac{1}{x}$.

Putting the value of x = √5+2 in 1/x we have ;

$\frac{1}{\sqrt{5} + 2 }$

Step II : Multiply the numerator and denominator with the rationalizing factor

The rationalizing factor of √5+2 is √5-2. So;

$\frac{1}{\sqrt{5}+ 2}\\ = \frac{1(\sqrt{5} - 2)}{(\sqrt{5}+ 2)(\sqrt{5} - 2)}$

Step III : Simplify the equation;

$\frac{1(\sqrt{5} - 2)}{(\sqrt{5}+ 2)(\sqrt{5} - 2)}\\\\= \frac{\sqrt{5} - 2}{(\sqrt{5}) ^{2} - 2^{2} } ( a^{2} - b^{2})= (a-b)(a+b) \\= \frac{\sqrt{5} - 2}{5-4} \\= \frac{\sqrt{5} - 2}{1}$

= √5 - 2.

The solution is √5 - 2.

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