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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

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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

$2 over 7$

$7 over 8$

$7 over 2$

$8 over 7$

$7 over 8$

$2 straight x space plus space 2 over straight x space equals space 3$
$rightwards double arrow space space straight x space plus space 1 over straight x space equals space 3 over 2$
$rightwards double arrow space open parentheses straight x space plus space 1 over straight x close parentheses cubed space equals space open parentheses 3 over 2 close parentheses cubed rightwards double arrow space space straight x cubed space plus space 1 over straight x cubed space plus space 3 straight x space cross times space 1 over straight x open parentheses straight x plus 1 over straight x close parentheses space equals 27 over 8 rightwards double arrow space space space straight x cubed space plus space 1 over straight x cubed space plus space 3 space cross times space 3 over 2 space equals space 27 over 8 rightwards double arrow space space straight x cubed space plus space 1 over straight x cubed space plus space 2 space equals space 27 over 8 minus 9 over 2 plus 2$

$rightwards double arrow space straight x cubed space plus space 1 over straight x cubed space plus 2 space equals space fraction numerator 27 minus 36 plus 16 over denominator 8 end fraction rightwards double arrow space space straight x cubed plus 1 over straight x cubed plus 2 space equals space 7 over 8$

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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: