Question

Find the value of 8x 3 +27y 3 , if 2x+3y =8 and xy =2

Answer 1

2X+3Y = 8
8X³+27Y³ = (2X)³+(3Y)³
= (2X+3Y) × ((2X)²–2X×3Y+(3Y)²)
= 8 × ((2X+3Y)²–2×2X×3Y–6XY)
= 8 × (8²–18×2)
= 8×(64–36)
= 8×28
= 224

Answer 2

$\bf \red{8 {x}^{3} + 27 {y}^{3} = 224}$

Given:

• $2x + 3y = 8$ and
• $xy = 2$

To find:

• Find the value of $8 {x}^{3} + 27 {y}^{3}$

Solution:

Identity to be used:

$\bf ( {a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b)$

Step 1:

Let $2x + 3y = 8...eq1$

and $xy = 2...eq2$

Take cube of eq1 in both sides

$( {2x + 3y)}^{3} = 512$

Step 2:

Compare with identity and open identity.

It is clear that

a= 2x and b = 3y

Open identity.

${(2x)}^{3} + {(3y)}^{3} + 3(2x)(3y)(2x + 3y) = 512$

or

$8 {x}^{3} + 27 {y}^{3} + 18xy(2x + 3y) = 512$

or

put the values from eq1 and eq2

$8 {x}^{3} + 27 {y}^{3} + 18(2)(8) = 512$

or

$8 {x}^{3} + 27 {y}^{3} + 288 = 512$

or

$8 {x}^{3} + 27 {y}^{3} = 512 - 288$

or

$8 {x}^{3} + 27 {y}^{3} = 224$

Thus,

$\bf 8 {x}^{3} + 27 {y}^{3} = 224$

Learn more:

1) If x+y =12 and xy= 27, find the value of x3 + y3

https://brainly.in/question/1275638

2) if 2x +3y=12 and xy=6 find the value of 8x³+27y³

https://brainly.in/question/8734295