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If $fraction numerator straight a over denominator 1 minus 2 straight a end fraction space plus space fraction numerator straight b over denominator 1 minus 2 straight b end fraction space plus space fraction numerator straight c over denominator 1 minus 2 straight c end fraction space equals space 1 half$ , then the value of $fraction numerator 1 over denominator 1 minus 2 straight a end fraction space plus space fraction numerator 1 over denominator 1 minus 2 straight b end fraction space plus space fraction numerator 1 over denominator 1 minus 2 straight c end fraction$ is

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152.
If x = 999, y = 1000, z = 1001, then the value of $fraction numerator straight x cubed plus straight y cubed plus straight z cubed minus 3 xyz over denominator straight x minus straight y plus straight z end fraction$ is

1000

9000

1

1

$fraction numerator straight x cubed plus straight y cubed plus straight z cubed minus 3 xyz over denominator straight x minus straight y plus straight z end fraction$

$fraction numerator begin display style 1 half left parenthesis straight x plus straight y plus straight z right parenthesis thin space open square brackets open parentheses left parenthesis straight x minus straight y right parenthesis squared space plus space left parenthesis straight y minus straight z right parenthesis squared close parentheses space plus space left parenthesis straight z minus straight x right parenthesis squared close square brackets end style over denominator straight x minus straight y plus straight z end fraction$

$equals space fraction numerator begin display style 1 half end style open square brackets 999 plus 1000 plus 1001 close square brackets space open square brackets open parentheses 999 minus 1000 close parentheses squared space left parenthesis 1000 minus 1001 right parenthesis squared space plus space left parenthesis 1001 minus 999 right parenthesis squared close square brackets over denominator 999 minus 1000 plus 1001 end fraction equals space 1 half space cross times space fraction numerator 3000 left square bracket 1 plus 1 plus 4 right square bracket over denominator 1000 end fraction equals space 1 half space cross times space fraction numerator 3000 space cross times space 6 over denominator 1000 end fraction equals space 9$

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153.

If $straight p squared space plus space 1 over straight p squared space equals space 47 comma$ then value of $straight p plus 1 over straight p$ is

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154.

If $straight x plus square root of 5 space equals space 5 space plus space square root of straight y$ and x, y are positive integers, then the value of $fraction numerator square root of straight x plus straight y over denominator straight x plus square root of straight y end fraction space is colon$

1
2
$square root of 5$
5

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155.

If (x - 2) (x - p) = x² - ax + 6, then the value of (a - p) is:

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156.

When $2 straight x plus 2 over straight x space equals space 3 comma$ then value of $straight x cubed space plus space 1 over straight x cubed plus 2$ is

$2 over 7$
$7 over 8$
$7 over 2$
$8 over 7$

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157.

If $straight x space equals space square root of straight a space plus space fraction numerator 1 over denominator square root of straight a end fraction comma space space space straight y space equals space square root of straight a space minus space fraction numerator 1 over denominator square root of straight a end fraction comma space space left parenthesis straight a space space greater than space 0 space right parenthesis$ then the value of x⁴ + y⁴ - 2x²y² is

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158.

If $straight x space equals space cube root of straight x squared plus 11 minus 2 end root comma$ then the value of x³ + 5x² + 12x is

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159.

If $straight x space plus space 1 over straight x space equals space 5 comma$ then the value of $fraction numerator 5 straight x over denominator straight x squared space plus space 5 straight x space plus space 1 end fraction$ is:

$1 third$
$1 fourth$
$1 half$
$1 fifth$

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160.

If $1 over straight a left parenthesis straight a squared plus 1 right parenthesis space equals space 3 comma$ then the value of $fraction numerator straight a to the power of 6 plus 1 over denominator straight a cubed end fraction$ is: