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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

42 Views

182.

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

54 Views

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

4

8

16

64

$straight x space equals space space straight a space space plus space 1 over straight a space space and space straight y space equals space straight a space minus space 1 over straight a$
x⁴ + y⁴ - 2x²y² = (x² - y²)²
= [(x + y) (x - y)]²
$equals space open square brackets open parentheses straight a space plus space 1 over straight a space plus space straight a space minus space 1 over straight a close parentheses space open parentheses straight a space plus space 1 over straight a space minus space straight a space plus space 1 over straight a close parentheses close square brackets squared space equals space open square brackets 2 straight a space cross times space 2 over straight a close square brackets squared space equals space left parenthesis 4 right parenthesis squared space equals space 16$

41 Views

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:

$1 over 6$
$1 third$
$negative 1 over 6$
$negative 1 third$

55 Views

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

73 Views

186.

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

999999
1000000
1000001
999998

244 Views

187.

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

57 Views

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

45 Views

189.

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

45 Views

190.

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