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If $fraction numerator 3 over denominator left parenthesis straight x plus 2 right parenthesis thin space left parenthesis 2 straight x plus 1 right parenthesis end fraction space space equals space fraction numerator straight a over denominator 2 straight x plus 1 end fraction space plus space fraction numerator straight b over denominator straight x plus 2 end fraction$ be an identity, then the value of b is

0
-1
2
3

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182.

If a + b = 5 and a - b = 3, then the value of (a² + b²) is

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183.

If $straight x space equals space straight a space plus space 1 over straight a$ and $straight y space equals space straight a space minus space 1 over straight a comma$ the value of x⁴ + y⁴ - 2x²y² is

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184.
If x² + 5x + 6 = 0, then the value of $fraction numerator 2 straight x over denominator straight x squared minus 7 straight x plus 6 end fraction$ is:

$1 over 6$

$1 third$

$negative 1 over 6$

$negative 1 third$

$negative 1 over 6$

x² + 5x+ 6
Divide the whole equation by x:
$rightwards double arrow space space straight x space space plus space 5 space plus space 6 over straight x space equals space 0 rightwards double arrow space space space straight x space plus space 6 over straight x space equals space minus 5 space space space space space space space space space... left parenthesis straight i right parenthesis$

$fraction numerator 2 straight x over denominator straight x squared minus 7 straight x plus 6 end fraction$
Again divide the whole equation by x:
$rightwards double arrow space space fraction numerator 2 over denominator straight x minus 7 plus begin display style 6 over straight x end style end fraction space equals space fraction numerator 2 over denominator straight x plus begin display style 6 over straight x end style minus 7 end fraction equals space fraction numerator 2 over denominator negative 5 minus 7 end fraction space equals space fraction numerator negative 2 over denominator 12 end fraction space equals space minus 1 over 6 space space space left square bracket Using space left parenthesis straight i right parenthesis right square bracket$

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185.

If $straight a over straight b space plus space straight b over straight a space equals space 1 comma$ then the value of a³ + b³ will be

1
0
-1
2

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186.

If p = 99, then the value of p(p² + 3p + 3) will be

999999
1000000
1000001
999998

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187.

If a - b = 1 and a³ - b³ = 61, the the value of ab will be

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188.

If $fraction numerator straight x over denominator straight x plus straight b end fraction space plus space 1 space equals space fraction numerator straight x over denominator straight a minus straight b end fraction space plus space fraction numerator straight a minus straight b over denominator straight a plus straight b end fraction comma$ then x is equal to

2a - b
a + b
a - b
2a + b

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189.

If x² - 4x + 1 = 0, the value of $fraction numerator straight x to the power of 6 plus 1 over denominator straight x cubed end fraction space is$ :

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190.

If a² = b + c, b² = c + a, c² = a + b, then the value of:
$3 open parentheses fraction numerator 1 over denominator straight a plus 1 end fraction space plus space fraction numerator 1 over denominator straight b plus 1 end fraction space plus space fraction numerator 1 over denominator straight c plus 1 end fraction close parentheses$