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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

26 Views

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

$square root of 3$

$square root of 6$

2

$square root of 2$

$straight x space equals space fraction numerator 2 square root of 6 over denominator square root of 3 space plus space square root of 2 end fraction$
or
$fraction numerator straight x over denominator square root of 2 end fraction space equals space fraction numerator 2 square root of 3 over denominator square root of 3 begin display style plus end style begin display style square root of 2 end style end fraction space space space space space... left parenthesis straight i right parenthesis$
Now, the value of
$fraction numerator straight x space plus space square root of 2 over denominator straight x space minus space square root of 2 end fraction$
Divide by the numerator and denominator by $square root of 2$
$fraction numerator begin display style fraction numerator straight x over denominator square root of 2 end fraction space plus space 1 end style over denominator begin display style fraction numerator straight x over denominator square root of 2 end fraction minus 1 end style end fraction$
$rightwards double arrow space space space fraction numerator begin display style fraction numerator 2 square root of 3 over denominator square root of 3 space plus space square root of 2 end fraction end style space plus space 1 over denominator begin display style fraction numerator 2 square root of 3 over denominator square root of 3 plus square root of 2 end fraction end style minus 1 end fraction space equals space fraction numerator 2 square root of 3 space plus space square root of 3 space plus space square root of 2 over denominator 2 square root of 3 minus square root of 3 minus square root of 2 end fraction space space space space left square bracket using space left parenthesis straight i right parenthesis right square bracket$
∴ The value of $fraction numerator straight x plus square root of 2 over denominator straight x minus square root of 2 end fraction$ is $space fraction numerator 3 square root of 3 space plus space square root of 2 over denominator square root of 3 space minus space square root of 2 end fraction$ ...(ii)
Similarly, The value of $fraction numerator straight x plus square root of 3 over denominator straight x minus square root of 3 end fraction space equals space minus fraction numerator 3 square root of 2 space plus space square root of 3 over denominator square root of 3 begin display style minus end style begin display style square root of 2 end style end fraction space space space space space space space space space space space... left parenthesis iii right parenthesis$
Add (ii) and (iii), we get
$fraction numerator straight x plus square root of 2 over denominator straight x minus square root of 2 end fraction plus space fraction numerator straight x plus square root of 3 over denominator straight x minus square root of 3 end fraction space equals space fraction numerator 3 square root of 3 space plus space square root of 2 over denominator square root of 3 begin display style minus end style begin display style square root of 2 end style end fraction space minus space fraction numerator 3 square root of 2 plus square root of 3 over denominator square root of 3 begin display style minus end style begin display style square root of 2 end style end fraction space equals space fraction numerator 2 left parenthesis square root of 3 minus square root of 2 right parenthesis over denominator square root of 3 begin display style minus end style begin display style square root of 2 end style end fraction space equals space 2$

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220. If then the value of is 2