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If $straight a squared space plus space 1 over straight a squared space equals space 98 space left parenthesis straight a space greater than space 0 right parenthesis comma$ then the value of $straight a cubed space plus space 1 over straight a cubed$ will be

535
1030
790
970

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212.

If 4x = 18y, then the value of $open parentheses straight x over straight y minus 1 close parentheses$ is

$1 third$
$7 over 2$
$2 over 3$
$3 over 2$

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213.

If $straight x space plus space 1 over straight x space equals space 5 comma$ then the value of $fraction numerator straight x to the power of 4 space plus space begin display style 1 over straight x squared end style over denominator straight x squared space minus space 3 straight x space plus space 1 end fraction$ is

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214.

If $straight x space equals space 1 plus square root of 2 space plus space square root of 3 comma space space$ then the value of (2x⁴ - 8x³ - 5x² + 26x - 28) is

$6 square root of 6$
0
$3 square root of 6$
$2 square root of 6$

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215.

If a + b = 6, a - b = 2, then the value of 2(a² + b²) is

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216.

If $straight a space equals space fraction numerator 2 plus square root of 3 over denominator 2 minus square root of 3 end fraction$ and $straight b space equals space fraction numerator 2 minus square root of 3 over denominator 2 plus square root of 3 end fraction comma$ then the value of (a² + b² + ab) is

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217.

If $straight x space equals space fraction numerator 1 over denominator 2 plus square root of 3 end fraction comma space space space straight y space equals space fraction numerator 1 over denominator 2 minus square root of 3 end fraction comma$ then the value of $fraction numerator 1 over denominator straight x plus 1 end fraction space plus space fraction numerator 1 over denominator straight y plus 1 end fraction$ is

$square root of 3$
1
$fraction numerator 1 over denominator square root of 3 end fraction$
$1 half$

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218.

If $square root of fraction numerator straight x minus straight a over denominator straight x minus straight b end fraction end root space plus space straight a over straight x space equals space square root of fraction numerator straight x minus straight b over denominator straight x minus straight a end fraction end root space plus space straight b over straight x comma space space straight b not equal to straight a comma space$ then the value of x is

$fraction numerator ab over denominator straight a plus straight b end fraction$
1
$fraction numerator straight a over denominator straight a space plus space straight b end fraction$
$fraction numerator straight b over denominator straight a space plus space straight b end fraction$

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219.
If $straight x space equals space fraction numerator 2 square root of 24 over denominator square root of 3 space plus space square root of 2 end fraction comma$ then the value of $fraction numerator straight x space plus space square root of 8 over denominator straight x space minus space square root of 8 end fraction space plus space fraction numerator straight x space plus space square root of 12 over denominator straight x space minus space square root of 12 end fraction$ is

2

0

-2

1

Given,
$straight x space equals space fraction numerator 2 square root of 24 over denominator square root of 3 space plus space square root of 2 end fraction space$
$rightwards double arrow space space fraction numerator straight x over denominator square root of 8 end fraction space space equals space fraction numerator 1 over denominator square root of 8 end fraction space cross times space fraction numerator 2 space cross times space space 2 space cross times space square root of 3 space cross times square root of 2 over denominator square root of 3 begin display style space end style begin display style plus end style begin display style space end style begin display style square root of 2 end style end fraction rightwards double arrow space space fraction numerator straight x over denominator square root of 8 end fraction space equals space fraction numerator 1 over denominator 2 square root of 2 end fraction cross times space fraction numerator begin display style 2 space cross times space space 2 space cross times space square root of 3 space cross times square root of 2 end style over denominator begin display style square root of 3 space plus space square root of 2 end style end fraction$
$rightwards double arrow space space space space space fraction numerator straight x over denominator square root of 8 end fraction space equals space fraction numerator 2 square root of 3 over denominator square root of 3 space plus space square root of 2 end fraction$
Now,
$fraction numerator straight x space plus space square root of 8 over denominator straight x minus square root of 8 end fraction$
Divide the numerator and denominator by $square root of 8$
$fraction numerator begin display style fraction numerator straight x over denominator square root of 8 end fraction space plus space 1 end style over denominator begin display style fraction numerator straight x over denominator square root of 8 end fraction minus 1 end style end fraction$
$equals space fraction numerator begin display style fraction numerator 2 square root of 3 over denominator square root of 3 plus square root of 2 end fraction end style space plus space 1 over denominator begin display style fraction numerator 2 square root of 3 over denominator square root of 3 plus square root of 2 end fraction end style space minus 1 end fraction equals space fraction numerator 2 square root of 3 space plus space square root of 3 space plus space square root of 2 over denominator square root of 3 plus space square root of 2 end fraction space equals space 1$

$therefore space space space space fraction numerator straight x plus square root of 8 over denominator straight x minus square root of 8 end fraction space equals space 1 space space space space space space... left parenthesis straight i right parenthesis$
Similarly,
$fraction numerator straight x space plus space square root of 12 over denominator straight x minus square root of 12 end fraction space equals space 1 space space space space space space... left parenthesis ii right parenthesis$
Add eqn (i) and (ii), we get 2.
∴ 2 is the required answer.

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220.

If $straight x space equals space fraction numerator 2 square root of 6 over denominator square root of 3 space plus space square root of 2 end fraction comma$ then the value of $fraction numerator straight x plus square root of 2 over denominator straight x minus square root of 2 end fraction space plus space fraction numerator straight x plus square root of 3 over denominator straight x minus square root of 3 end fraction$ is