Question

answer with photos pls​

Answer 1

Question : If 3x - 2y = 11 and xy = 12, find the value of 27x³ - 8y³.

Answer:

$\large{\underline{\boxed{\sf 27x^{3} - 8y^{3} = 3707}}}$

Step-by-step explanation:

$\large{\underline{\underline{\sf \star \: Given \: that :}}}$

3x - 2y = 11 .... (i)

xy = 12 .... (ii)

On cubing both sides equation (i) -

(3x - 2y)³ = (11)³

⇒ (3x)³ - (2y)³ - 3 * 3x * 2y (3x - 2y) = 1,331

[ ∵ (a - b)³ = a³ - b³ - 3ab(a - b)]

⇒ 27x³ - 8y³ - 18 xy (11) = 1,331

⇒ 27x³ - 8y³ - 18 * 12 * 11 = 1,331

⇒ 27x³ - 8y³ - 2,376 = 1,331

⇒ 27x³ - 8y³ = 1,331 + 2,376

⇒ 27x³ - 8y³ = 3,707

Hence, the answer is 3,707.

_________________________________

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

• (x + y)³ = x³ + y³ + 3xy(x + y)
• (x - y)³ = x³ - y³ - 3xy(x - y)
• (x + y)² = x² + 2xy + y²
• (x - y)² = x² - 2xy + y²

Answer 2

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

$\boxed{\bold{27 {x}^{3} - 8 {y}^{3} = 3707}}$

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$ :

Given : 1) 3x - 2y = 11

2) xy = 12

To find : 27x³ - 8y³

Solution :

3x - 2y = 11

By cubing on both the sides

${(3x - 2y)}^{3} = {11}^{3}$

[ Since (a - b)³ = a³ - b³ - 3ab(a - b) ]

Here a = 3x, b = 2y

By substituting the values

${(3x)}^{3} - {(2y)}^{3} - 3(3x)(2y)(3x - 2y) = 1331$

$27 {x}^{3} - 8 {y}^{3} - 18xy(11) = 1331$

[Since Given that (3x - 2y) = 11]

$27 {x}^{3} - 8 {y}^{3} - 18(12)(11) = 1331$

[Since Given that xy = 12]

$27 {x}^{3} - 8 {y}^{3} - 2376 = 1331$

$27 {x}^{3} - {8y}^{3} =1331 + 2376$

$27 {x}^{3} - 8 {y}^{3} = 3707$

$\boxed{\bold{27{x}^{3} - 8 {y}^{3} = 3707}}$

$\mathfrak{\large{\underline{\underline{Identity\:used:-}}}}$

(a - b)³ = a³ - b³ - 3ab(a - b)

$\mathfrak{\large{\underline{\underline{Extra\:information-}}}}$

What is an Identity ?

An equation is called an identity if it is satisfied by any value that replaces its variables.

$\mathfrak{\large{\underline{\underline{Some\:Important\:Identities:-}}}}$

1] (x + y)² = x² + 2xy + y²

2] (x - y)² = x² - 2xy + y²

3] (x + y)(x - y) = x² - y²

4] (x + a)(x + b) = x² + (a + b)x + ab