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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

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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

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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

-1

$straight a space plus space 1 over straight b space equals space 1 rightwards double arrow space fraction numerator ab space plus space 1 over denominator straight b end fraction space equals space 1 rightwards double arrow space space space ab space plus space 1 space equals space straight b space space space space space space space space space space space space space space space space space space$
Multiply by c on both sides
$rightwards double arrow space abc space plus space straight c space equals space bc space space space space space... left parenthesis straight i right parenthesis$
$straight b space plus space 1 over straight c space equals space 1 rightwards double arrow space fraction numerator bc space plus space 1 over denominator straight c end fraction space equals space 1 rightwards double arrow space space bc space plus space 1 space equals space straight c space space space space space... left parenthesis ii right parenthesis$
From (i) and (ii),
abc + bc + 1 = bc
$rightwards double arrow space space abc space equals space bc space minus space bc space minus space 1 rightwards double arrow space space abc space equals space minus 1$

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

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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