Given expression
= [(a + b)² + (a - b)²] / [a² + b²]
= 2(a² + b²) / (a² + b²)

Correct Option: B

Given expression
= [(a + b)² + (a - b)²] / [a² + b²]
= 2(a² + b²) / (a² + b²)
= 2
where, a = 238, b = 131

Given expression
= [(a + b )² - (a - b )²] / ab

Correct Option: D

Given expression
= [(a + b )² - (a - b )²] / ab
= 4ab/ab
= 4
where, a = 999, b = 588

Given expression
[a³ + b³ + c³ - 3abc] / [a² + b² + c² - ab - bc - ca]
= a + b + c

Correct Option: A

Given expression
[a³ + b³ + c³ - 3abc] / [a² + b² + c² - ab - bc - ca]
= a + b + c
= 0.5 + 0.2 + 0.3
where, a = 0.5, b = 0.2, c = 0.3

? = [5 -[3/4 + {2¹/₂ - (1/2 + 1/6 - 1/7)}]]/2
= [5 - [3/4 + {5/2 -(1/2 + 7 - 6/42)}]]/2
= [5 - [3/4 + {5/2 - (1/2 + 1/42)}]]/2
= [5 - [3/4 + {5/2 - (21 + 1 /42)}]]/2

Correct Option: A

? = [5 -[3/4 + {2¹/₂ - (1/2 + 1/6 - 1/7)}]]/2
= [5 - [3/4 + {5/2 -(1/2 + 7 - 6/42)}]]/2
= [5 - [3/4 + {5/2 - (1/2 + 1/42)}]]/2
= [5 - [3/4 + {5/2 - (21 + 1 /42)}]]/2
= [5 - [3/4 + {5/2 - 22/42}]]/2
= [5 - [3/4 + {105 - 22/42}]]/2
= [5 - [3/4 + 83/42]] / 2
= [5 - [63 + 166/84]]/2
= (191/84)/2
=191/168 = 1²³/₁₆₈

We know that,
(a + b + c)² = (a² + b² + c²) + 2(ab + bc + ca )
⇒ 196 = 96 + 2(ab + bc + ca)
⇒ 2(ab + bc + ca) = 196 - 96 = 100

Correct Option: C

We know that,
(a + b + c)² = (a² + b² + c²) + 2(ab + bc + ca )
⇒ 196 = 96 + 2(ab + bc + ca)
⇒ 2(ab + bc + ca) = 196 - 96 = 100
∴ (ab + bc + ca) = 100/2 = 50