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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

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

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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

16

20

10

5

$straight x space equals space square root of straight a space plus space fraction numerator 1 over denominator square root of straight a end fraction comma space space space straight y space equals square root of straight a space minus space fraction numerator 1 over denominator square root of straight a end fraction$
$straight x to the power of 4 space plus space straight y to the power of 4 space minus space 2 straight x squared straight y squared space equals space left parenthesis straight x squared minus straight y squared right parenthesis squared equals space open square brackets open parentheses straight x minus straight y close parentheses left parenthesis straight x space plus space straight y right parenthesis close square brackets squared equals space open square brackets open parentheses square root of straight a space plus space fraction numerator 1 over denominator square root of straight a end fraction minus square root of straight a plus fraction numerator 1 over denominator square root of straight a end fraction close parentheses space open parentheses square root of straight a space plus space fraction numerator 1 over denominator square root of straight a end fraction plus square root of straight a minus fraction numerator 1 over denominator square root of straight a end fraction close parentheses close square brackets squared equals space open square brackets fraction numerator 2 over denominator square root of straight a end fraction space cross times space 2 square root of straight a close square brackets squared space equals space left parenthesis 4 right parenthesis squared equals space 16$

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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: