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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

40 Views

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

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

$5 over 12$

$12 over 5$

$5 over 7$

$7 over 5$

$12 over 5$

$fraction numerator square root of 3 plus straight x end root space plus space square root of 3 minus straight x end root over denominator square root of 3 plus straight x end root space minus square root of 3 minus straight x end root end fraction space equals space 2$
$Let space space space space square root of 3 plus straight x end root space equals space straight a comma space space space square root of 3 minus straight x end root space equals space straight b$
$rightwards double arrow space space space fraction numerator straight a space plus space straight b over denominator straight a space minus space straight b end fraction space equals space 2 rightwards double arrow space space space straight a space plus space straight b space equals space 2 straight a space minus space 2 straight b rightwards double arrow space space space space straight a space equals space 3 straight b rightwards double arrow space space space space square root of 3 plus straight x end root space equals space 3 square root of 3 minus straight x end root$
On squaring both sides, we get
3 + x = 9(3 - x)
$rightwards double arrow space space space space 3 space space plus space straight x space equals space 27 space minus space 9 straight x rightwards double arrow space space space space 9 straight x space plus space straight x space equals space 27 space minus space 3 rightwards double arrow space space space space space space space space 10 straight x space equals space space 24 rightwards double arrow space space space space space space space space straight x space equals space 24 over 10 space equals space 12 over 5 space space space$