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If $left parenthesis straight a minus 2 right parenthesis space plus space fraction numerator 1 over denominator left parenthesis straight a space plus space 2 right parenthesis end fraction space equals space minus 1$ , then the value of $left parenthesis straight a plus 2 right parenthesis squared space plus space fraction numerator 1 over denominator left parenthesis straight a plus 2 right parenthesis squared end fraction$ is

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192.

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

0
1
-1
2

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193.

If x = at² and y = 2at then

x² = 4ay
y² = 4ax
x² + y² = a²
x² - y² = a²

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194.

If xy + yz + zx = 1, then the value of $fraction numerator 1 plus straight y squared over denominator left parenthesis straight x plus straight y right parenthesis thin space left parenthesis straight y plus straight z right parenthesis end fraction$ is

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195.

If $5 straight x space plus space 1 over straight x space equals space 10 comma$ then $straight x squared space plus space fraction numerator 1 over denominator 25 straight x squared end fraction$ is equal to

$2 1 fifth$
$3 1 fifth$
$3 3 over 5$
$2 3 over 5$

196.

If a + b = 3 then the value of a³ + b³ + 9ab - 27 is

197.
If $straight x space plus space 1 over straight x space equals space 2 comma$ then the value of $straight x to the power of 7 space plus space 2 over straight x to the power of 6$ is equal to

0

1

2

3

Put the value of x = 1 as, it satisfies the equation,
$rightwards double arrow space space space straight x plus 1 over straight x space equals space 2 rightwards double arrow space space space 1 space plus space 1 over 1 space equals space 2 rightwards double arrow space space space space space space 2 space equals space 2 space space$
$therefore space space space space straight x to the power of 7 space plus space 2 over straight x to the power of 6 space space equals space left parenthesis 1 right parenthesis to the power of 7 space plus space fraction numerator 2 over denominator left parenthesis 1 right parenthesis to the power of 6 end fraction space equals space 1 space plus space 2 space space equals space 3$

198.

If a = 11 and b = 9, then the value of $open parentheses fraction numerator straight a squared plus straight b squared plus ab over denominator straight a cubed minus straight b cubed end fraction close parentheses$ is

$1 half$
2
$1 over 20$
20

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199.

If $fraction numerator square root of 3 plus straight x end root space plus space square root of 3 minus straight x end root over denominator square root of 3 plus straight x end root space minus space square root of 3 minus straight x end root end fraction space equals space 2$ , then x is equal to