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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

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

48 Views

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

29 Views

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

$3 square root of 6$

$2 square root of 6$

$6 square root of 6$

$straight x space equals space space 1 space plus space square root of 2 space plus space square root of 3 rightwards double arrow space space straight x space minus space 1 space equals space square root of 2 space plus space square root of 3$
S.B.S.
$rightwards double arrow space space space left parenthesis straight x space minus space 1 right parenthesis squared space equals space left parenthesis square root of 2 space plus space square root of 3 right parenthesis squared rightwards double arrow space space space straight x squared space minus 2 straight x space plus space 1 space equals space 2 space plus space 3 space plus space 2 square root of 6 rightwards double arrow space space space space straight x squared minus 2 straight x space equals space 4 space plus space 2 square root of 6 rightwards double arrow space space space space straight x squared space minus space 2 straight x space minus space 4 space equals space 2 square root of 6 space space space space space space space space space space space space space space space space space space space$
Again, S.B.S.
$rightwards double arrow space space space space space space left parenthesis straight x squared minus 2 straight x minus 4 right parenthesis squared space equals space left parenthesis 2 square root of 6 right parenthesis squared space space space space space open curly brackets therefore space left parenthesis straight a space plus space straight b space plus space straight c right parenthesis squared space equals space straight a squared space plus space straight b squared space plus space straight c squared space plus space 2 ab space plus space 2 bc space plus space 2 ca close curly brackets rightwards double arrow space space space space space straight x to the power of 4 minus 4 straight x squared space plus space 16 space minus space 4 straight x cubed space plus space 16 straight x space minus space 8 straight x squared space equals space 24 rightwards double arrow space space space space space straight x to the power of 4 space minus 4 straight x cubed space minus space 4 straight x squared space plus space 16 straight x space minus space 8 space equals space 0 rightwards double arrow space space space space space 2 straight x to the power of 4 space minus space 8 straight x cubed space minus space 8 straight x squared space plus space 32 straight x space minus space 16 space equals space 0 rightwards double arrow space space space space 2 straight x to the power of 4 space minus space 8 straight x cubed space minus space 5 straight x squared space plus space 26 straight x space minus space 28 space equals space 3 straight x squared space minus space 6 straight x minus space 12$

$equals space 3 left parenthesis straight x squared space minus space 2 straight x right parenthesis space minus space 12 space equals space 3 left parenthesis 4 plus 2 square root of 6 right parenthesis minus 12 equals space 12 space plus space 6 square root of 6 space minus space 12 space equals space 6 square root of 6$

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215.

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

29 Views

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

27 Views

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

28 Views

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

31 Views

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