3x + 2y = 12 and xy = 6, them the value of 9x² + 4y² is?

(4 x 4 x 4 x 4 x 4 x 4)⁵ x (4 x 4 x 4)⁸ ÷ (4)³ = (64)^?
Apply the law of Fractional Exponents and Laws of Exponents
if a multiply n times a x a x a x....up to n times, then
a x a x a x a ......up to n times = aⁿ
By simplifying the equation
? (4⁶)⁵ x (4³)⁸ x 1/(4)³ = (4³)^?
? (4)³⁰ x (4)²⁴/(4)³ = (4)^{3 x ?}
? 4^{30 + 24 - 3} = 4^{3 x 7}
And comparing the exponents both the sides
? 4⁵¹ = 4^{3 x ?} ? 3 x ? = 51
? ? = 51/3 = 17

Since a * b = a + b + a / b
? 12 * 4 = 12 + 4 + 12 / 4
= 12 + 4 + 3 = 19

a² + 1 = a ? a + 1/a = 1
On squaring both sides, we get
a² + 1/a² + 2 = 1
? a² + 1/a² = -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 also be written as a⁶ + 1/a⁶ + 1
? a¹² + a⁶ + 1 = 3

We know that, a³ + b³ + c³ - 3abc
= (a + b + c) (a² + b² + c² - ab - bc - ca)
? (a + b + c) = (a³ + b³ + c³ - 3abc/a² + b² + c² - ab - bc - ca) ....(i)
Given that,
(2.247)³ + (1.730)³ + (1.023)³ - 3 x 2.247 x 1.730 x 1.023/ (2.247)² + (1.730)² + (1.023)² - (2.247 x 1.730) - (1.730 x 1.023) - (2.247 x 1.023)
= 2.247 + 1.730 x 1.023) - (2.247 x 1.023)
= (2.247 + 1.730 + 1.023) [from Eq.(i)]
= 5.000 = 5

? = 5 - [3/4 + {5/2 - (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
= 5 - 229/84/2 = 420 - 229/84/2 = 191/84/2
= 191/84 x 2 = 191/168 = 1²³/₁₆₈

x + 1/x = 3 ........................ (i)
On squaring both side, we will get
(x + 1/x)² = (3)²
Use the Square algebra formula (a + b)² = a² + 2ab + b²
? x² + 1/x² + 2 = 9
? x² + 1/x² = 7 ..................(ii)
Again squaring both sides, we will get
(x² + 1/x²)² = (7)²
Use the Square algebra formula (a + b)² = a² + 2ab + b²
? x⁴ + 1/⁴ + 2 = 49
? x⁴ + 1/x⁴ = 47 .....................(iii)
On cubing the equation (i) both side, we will get
(x + 1/x)³ = (3)³
Use the cube algebra formula (a + b)³ = a³ + 3a²b + 3ab² + b³
? x³+ 1/x³ + 3(x + 1/x) = 27
? x³ + 1/x³ + 9 = 27 [? (x + 1/x) = 3]
? x³ + 1/x³ = 18 ...................(iv)
On multiplying Eqs. (i) and (iii) , we get
? (x⁴ + 1/x⁴) (x + 1/x) = 47 x 3
? x⁵ + 1/x⁵ + x³ + 1/x³ = 141
? x⁵ + 1/x⁵ + 18 = 141 [from Eq. (iv)]
? x⁵ + 1/x⁵ = 123

Given that, x + 1/x = 2 ...................(i)
On squaring both sides, we get
(x + 1/x)² = 4
? x² + 1/x² + 2 = 4
? x² + 1/x² = 2 ..................................(ii)
Now, we have
(x - 1/x)² = (x² + 1/x²) - 2x X 1/x
now put the value of x² + 1/x²
(x - 1/x)² = 2 - 2 = 0 [from Eq. (ii)]
? x - 1/x = 0

x + 1/x = 6
On squaring both sides, we get
(x + 1/x)² = (6)²
? x² + 1/x² + 2 = 36
? x² + 1/x² = 34
On squaring both sides, we get
(x² + 1/x²)² = (34)²
? x⁴ + 1/x⁴ + 2 = 1156
? x⁴ + 1/x⁴ = 1154

Given in question,
x + y = 18
By using algebraic formula
? x² + y² = (x + y)² - 2xy
Put the value of x + y and xy as per given question,
? x² + y² = (18)² - 2 x 72
? x² + y² = 324 - 144
? x² + y² = 180

We know that algebraic formula,
(x + y)³ = x³ + y³ + 3xy (x + y)
put the value of x + y in given equation. [ given, x + y = 1]
1 = x³ + y³ + 3xy X 1
? x³ + y³ + 3xy = 1