Question

3a+1/3a=7,find 27a^3+1/27a^3

Answer 1

322

Step-by-step explanation:

Given:

$3a + \dfrac{1}{3a} = 7$

To find:

$27 {a}^{3} + \dfrac{1}{27 {a}^{3}}$

Solution:

$3a + \dfrac{1}{3a} = 7 \\ \\ [\text{Cubing both side}] \\ \\ ({3a + \dfrac{1}{3a})}^{3} = {7}^{3} \\ \\ 27 {a}^{3} + \frac{1}{27 {a}^{3}} + 3.3a. \frac{1}{3a} (3a + \frac{1}{3a} ) = 343 \\ \\ 27 {a}^{3} + \frac{1}{27 {a}^{3}} + 3. \cancel{3a}. \frac{1}{ \cancel{3a}} (7 ) = 343 \\ \\ 27 {a}^{3} + \frac{1}{27 {a}^{3}} + 3. (7 ) = 343 \\ \\ 27 {a}^{3} + \frac{1}{27 {a}^{3}} + 21 = 343 \\ \\ 27 {a}^{3} + \frac{1}{27 {a}^{3}} = 343 - 21 \\ \\ 27 {a}^{3} + \frac{1}{27 {a}^{3}} = 322$

The required answer is 322.

${{\boxed{ \text{\blue{Some Important Algebra Formula}}}}}$

${(x + y)}^{3}={x}^{3}+{y}^{3}+ 3xy(x + y) \\ \\(x - y)^{3}={x}^{3}-{y}^{3}- 3xy(x - y)$

Answer 2

$\rule{200}3$

$\huge\tt{GIVEN:}$

• 3a + ⅓a = 7

$\rule{200}3$

$\huge\tt{TO~FIND:}$

• 27a³ + 1/27a³

$\rule{200}3$

$\huge\tt{SOLUTION:}$

↪3a + ⅓a = 7

↪(3a + 1/3a)³ = 7³ (Cubing both sides)

↪27a³ + 1/27a³ + 3.3a.1/3a(3a+1/3a) = 343

↪27a³ + 1/27a³ + 1/27a³ + 3.3.1/3a(7) = 343

↪27a³ + 1/27a³ + 3(7) = 343

↪27a³ + 1/27a³ + 21 = 343

↪27a³ + 1/27a³ = 343 - 21

↪27a³ + 1/27a³ = 322 (Answer)

$\rule{200}3$