Question

If 2a+3b-13 and ab=6.Find the value of 8a^3+27b^3

Answer 1

Correct question: If 2a + 3b = 13 and ab = 6. Find the value of 8a³ + 27b³.

Answer:

$\large{\underline{\boxed{\sf 8a^3 + 27b^3 = - 1235}}}$

Step-by-step explanation:

Given that ;

• ab = 6
• 2a + 3b =13

⇒ 2a + 3b = 13

On cubing both sides -

⇒ (2a + 3b)³ = (13)³

⇒ (2a)³ + (3b)³ + 3 * 2a * 3b (2a + 3b) = 169

⇒ 8a³ + 27b³ + 18ab (13) = 169

⇒ 8a³ + 27b³ + 18 * 6 * 13 = 169

⇒ 8a³ + 27b³ + 1404 = 169

⇒ 8a³ + 27b³ = 169 - 1404

⇒ 8a³ + 27b³ = - 1235

Hence, the answer is (-1235).

$\rule{300}{2}$

$\large{\underline{\underline{\mathfrak{\heartsuit \: Algebraic \: Identity : \: \heartsuit}}}}$

• (a - b)³ = a³ - b³ - 3ab (a - b)
• (a + b)³ = a³ + b³ + 3ab (a + b)
• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• (x + a)(x + b) = x² + x(a + b) + ab

Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer = -1235

$\rule{110}1$

$\huge\sf\blue{Given}$

➳ 2a + 3b = 13

➳ ab = 6

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

➢ 8a³ + 27b³

$\rule{110}1$

$\huge\sf\purple{Steps}$

On cubing both sides -

➳ (2a + 3b)³ = (13)³

➳ (2a)³ + (3b)³ + 3 * 2a * 3b (2a + 3b) = 169

➳ 8a³ + 27b³ + 18ab (13) = 169

➳ 8a³ + 27b³ + 18 * 6 * 13 = 169

➳ 8a³ + 27b³ + 1404 = 169

➳ 8a³ + 27b³ = 169 - 1404

➳$\sf\orange{ 8a^3 + 27b^3 = - 1235}$

$\underline{\bullet{\sf{ \;More\: Identities}}}$

☆ (a+b)² = a²+2ab+b²

☆ (a-b)² = a²-2ab+b²

☆ (a+b)(a-b) = a²-b²

$\rule{170}3$