If x -3 -2-2 -3- find x -1- xA- 21 -2-10 -3-6B- 21 -2-10 -3-6C- 12 -2-14 -3-6D- 3 -2-2 -3-6

The correct option is B 21√(2) + 10√(3)/6 Given x nbsp;= 3√(2) + 2√(3). ∴ 1/x = 1/3√(2) + 2√(3) Rationalising factor of nbsp;3√(2) + 2√(3) = nbsp;3√( ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Natural Numbers

If x =3 √2+2 ...

Question

If $x = 3 \sqrt{2} + 2 \sqrt{3}$ , find $x + \frac{1}{x}$ .

$\frac{21 \sqrt{2} - 10 \sqrt{3}}{6}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{21 \sqrt{2} + 10 \sqrt{3}}{6}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$\frac{12 \sqrt{2} + 14 \sqrt{3}}{6}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{3 \sqrt{2} + 2 \sqrt{3}}{6}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
$\frac{21 \sqrt{2} + 10 \sqrt{3}}{6}$

Given $x$ = $3 \sqrt{2} + 2 \sqrt{3}$ .

$∴$ $\frac{1}{x}$ = $\frac{1}{3 \sqrt{2} + 2 \sqrt{3}}$

Rationalising factor of $3 \sqrt{2} + 2 \sqrt{3}$
= $3 \sqrt{2} - 2 \sqrt{3}$

Multiplying both numerator and denominator by $3 \sqrt{2} - 2 \sqrt{3}$ , we get

$\frac{(3 \sqrt{2} - 2 \sqrt{3})}{(3 \sqrt{2} + 2 \sqrt{3}) \times (3 \sqrt{2} - 2 \sqrt{3})}$

= $\frac{3 \sqrt{2} - 2 \sqrt{3}}{3^{2} \sqrt{(} 2)^{2} - 2^{2} \sqrt{(} 3)^{2}}$

= $\frac{3 \sqrt{2} - 2 \sqrt{3}}{18 - 12}$

So, $\frac{1}{x}$ = $\frac{3 \sqrt{2} - 2 \sqrt{3}}{6}$

$x + \frac{1}{x}$ = $3 \sqrt{2} + 2 \sqrt{3}$ + $\frac{3 \sqrt{2} - 2 \sqrt{3}}{6}$

= $\frac{18 \sqrt{2} + 12 \sqrt{3} + 3 \sqrt{2} - 2 \sqrt{3}}{6}$

= $\frac{21 \sqrt{2} + 10 \sqrt{3}}{6}$

Suggest Corrections

Similar questions

$\sqrt[4]{\sqrt[3]{2^{2}}}$ equals to

A.) $2^{\frac{- 1}{6}}$
B.) $2^{- 6}$
C.) $2^{\frac{1}{6}}$
D.) $2^{6}$

Q. Solve :
(i) |x

-

2| = 6

(ii) |3x

-

6| = 21

(iii) |4x

-

2| = 10

(iv) |

-

(2x

-

3) | = 7

(v) |x

-

\frac{1}{2}

| =

\frac{3}{2}

Q. Simplify:
(1)

\frac{m^{2} - n^{2}}{{(m + n)}^{2}} \times \frac{m^{2} + m n + n^{2}}{m^{3} - n^{3}}

(2)

\frac{a^{2} + 10 a + 21}{a^{2} + 6 a - 7} \times \frac{a^{2} - 1}{a + 3}

(3)

\frac{8 x^{3} - 27 y^{3}}{4 x^{2} - 9 y^{2}}

(4)

\frac{x^{2} - 5 x - 24}{(x + 3) (x + 8)} \times \frac{x^{2} - 64}{{(x - 8)}^{2}}

(5)

\frac{3 x^{2} - x - 2}{x^{2} - 7 x + 12} \div \frac{3 x^{2} - 7 x - 6}{x^{2} - 4}

(6)

\frac{4 x^{2} - 11 x + 6}{16 x^{2} - 9}

(7)

\frac{a^{3} - 27}{5 a^{2} - 16 a + 3} \div \frac{a^{2} + 3 a + 9}{25 a^{2} - 1}

(8)

\frac{1 - 2 x + x^{2}}{1 - x^{3}} \times \frac{1 + x + x^{2}}{1 + x}

Q. Find mode for the following data

:

$X$	$2 - 4$	$4 - 6$	$6 - 8$	$8 - 10$	$10 - 12$	$12 - 14$	$14 - 16$
$F$	$1$	$2$	$2$	$3$	$6$	$3$	$2$

Q. The value of

2 \frac{1}{10} - [1 \frac{2}{3} + {2 \frac{1}{3} - (1 \frac{1}{3} - \frac{1}{2})}]

Join BYJU'S Learning Program

If x=3√2+2√3, find x+1x .

If $x = 3 \sqrt{2} + 2 \sqrt{3}$ , find $x + \frac{1}{x}$ .