Question

2x + 3y = 13 and xy = 4, then the value of 8x3 + 27y3 is ___________?

Answer 1

Answer:

793

Step-by-step explanation:

2x +3y = 13-----(1)

xy =6-----(2)

8x³ +27y³  

= (2x)³ +(3y)³

= (2x+3y)³ - 3*2x*3y(2x+3y)  [using (a+b)³ = a³+b³+3ab(a+b)]

= (13)³- 18 * 6 *13 [ using (1) and (2)]

= 2197 - 1404

=793

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Answer 2

EXPLANATION.

⇒ 2x + 3y = 13. - - - - - (1).

⇒ xy = 4. - - - - - (2).

As we know that,

Formula of :

⇒ (a + b)³ = a³ + 3a²b + 3ab² + b³.

Using this formula in this question, we get.

Cubing on both sides of the equation (1), we get.

⇒ (2x + 3y)³ = (13)³.

⇒ (2x)³ + 3(2x)²(3y) + 3(2x)(3y)² + (3y)³ = 2197.

⇒ 8x³ + 3(4x²)(3y) + 3(2x)(9y²) + 27y³ = 2197.

⇒ 8x³ + 36x²y + 54xy² + 27y³ = 2197.

⇒ 8x³ + 27y³ + 36x²y + 54xy² = 2197.

⇒ 8x³ + 27y³ + 18xy(2x + 3y) = 2197.

Put the value of equation (1) and equation (2), we get.

⇒ 8x³ + 27y³ + 18(4)(13) = 2197.

⇒ 8x³ + 27y³ + 936 = 2197.

⇒ 8x³ + 27y³ = 2197 - 936.

⇒ 8x³ + 27y³ = 1261.

∴ The value of 8x³ + 27y³ is equal to 1261.