(?)² = ?13² + 28 / 4 - (3)³ + 107
= ?169 + 7 - 27 + 107
= ?256
= ?16
= 4

We know that, (a + b)² = a² + b² + 2ab
= 234 + 2 x 108 = 450
(a - b)² = a² + b² - 2ab
= 234 - 2 x 108 = 18
? (a + b)²/(a - b)² = 450/18 = 25
? [(a + b)/(a - b)]² = 25
? (a + b)/(a - b) = ?25 = 5

a² + 1 = a
? a + 1/a = 1
On squaring both sides, we get
a² + 1/a² + 2 = 1
On cubing both sides, we get
(a² + 1/a²)³ = (-1)³
? a⁶ + 1/a⁶ + 3a² x 1/a² (a² + 1/a²) = -1
? a⁶ + 1/a⁶ + 3 x (-1) = -1
Now, a⁶ + 1/a⁶ + 1 = 3
As, a¹² + a⁶ + 1 can be written as a⁶ + 1/a⁶ + 1
? a¹² + a⁶ + 1 = 3

? a + 1/b = 1
ab + 1 = b ...(i)

Also, b + 1/c = 1
? b = 1 - 1/c ...(ii)

From Eqs. (i) and (ii), we get
ab + a = 1 - 1/c
? ab = -1/c
? abc = -1

Since, a + b + c = 0
Then, a + b = -c ....(i)
a + c = -b .........(ii)
b + c = -a ....(iii)
Now, [(a + b)/c + (b + c)/a + (c + a)/b] x [a/(b + c) + b/(c + a) + c/(a + b)]
Now, putting the value of a + b , b + c and c + a from Eqs. (i), (ii) and (iii) , we get
[(-c)/c + (-a)/a + (-b)/b] x [a/-a + b/-b + c/-c]
[(-1) + (-1) + (-1)] [(-1) + (-1) + (-1)]
= (-3) x (-3) = 9

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

? = [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

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

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

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