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171.
If $straight x space plus space 1 over straight x space equals space square root of 13 comma space space then space fraction numerator 3 straight x over denominator left parenthesis straight x squared minus 1 right parenthesis end fraction$ equals to

$3 square root of 13$

$fraction numerator square root of 13 over denominator 3 end fraction$

1

3

$straight x space plus space 1 over straight x space equals space square root of 13$
If $straight x space plus space 1 over straight x space equals space straight a comma space space space then space straight x squared space plus space 1 over straight x squared space equals space straight a squared minus 2$
$therefore space space straight x squared space plus space 1 over straight x squared space equals space left parenthesis square root of 13 right parenthesis squared minus 2 space equals space 11$
Subtract 2 from both the sides,
$straight x squared space plus space 1 over straight x squared minus 2 space equals space 9 open parentheses straight x minus 1 over straight x close parentheses squared space equals space 9 straight x space minus space 1 over straight x space equals space 3$
Now,
$fraction numerator 3 straight x over denominator straight x squared minus 1 end fraction space equals space fraction numerator 3 straight x over denominator straight x open parentheses straight x minus begin display style 1 over straight x end style close parentheses space end fraction$
$equals space fraction numerator 3 over denominator open parentheses straight x minus begin display style 1 over straight x end style close parentheses end fraction space equals space 3 over 3 space equals space 1$

63 Views

172.

If $straight x space plus space 1 over straight x space equals space 2 comma$ then the value of $straight x to the power of 99 space plus space 1 over straight x to the power of 99 minus 2$ is:

-2
0
2
4

38 Views

173.

If $2 straight x space minus space fraction numerator 1 over denominator 2 straight x end fraction space equals space 5 comma$ $straight x not equal to 0$ then the value of $straight x squared space plus space fraction numerator 1 over denominator 16 straight x squared end fraction minus 2$ is

$19 over 4$
$23 over 4$
$27 over 4$
$31 over 4$

36 Views

174.

If $straight a space plus space 1 over straight b space equals space 1 comma space space space straight b space plus space 1 over straight c space equals space 1$ , then the value of abc is:

0
-1
1
ab

42 Views

175.

If $2 straight x space plus space fraction numerator 1 over denominator 4 straight x end fraction space equals space 1 comma$ then $straight x squared space plus space fraction numerator 1 over denominator 64 straight x squared end fraction$ is

0
1
$1 fourth$
2

41 Views

176.

If $square root of straight x space minus space square root of straight y space equals space 1 comma$ $square root of straight x space plus space square root of straight y space equals space 17 comma$ then $square root of xy space equals space ?$

$square root of 72$
72
32
24

35 Views

177.

If $straight x space equals space square root of 3 space plus space fraction numerator 1 over denominator square root of 3 end fraction comma$ then the value of $open parentheses straight x space minus space fraction numerator square root of 126 over denominator square root of 42 end fraction close parentheses space open parentheses straight x minus fraction numerator 1 over denominator straight x minus begin display style fraction numerator 2 square root of 3 over denominator 3 end fraction end style end fraction close parentheses space is colon$

$fraction numerator 5 square root of 3 over denominator 6 end fraction$
$fraction numerator 2 square root of 3 over denominator 3 end fraction$
$5 over 6$
$2 over 3$

42 Views

178.

If $straight c space plus space 1 over straight c space equals space 3 comma$ then the value of $left parenthesis straight c minus 3 right parenthesis to the power of 7 space plus space 1 over straight c to the power of 7$ is

43 Views

179.

If $straight a space equals space square root of 2 space plus space 1$ and $straight b space equals space square root of 2 minus 1 comma space$ then the value of $fraction numerator 1 over denominator straight a plus 1 end fraction space plus space fraction numerator 1 over denominator straight b plus 1 end fraction$ will be