Question

if 2 x minus 3 Y is equals to 10 and x y is equals to 16 find the value of 8 x cube minus 27 y cube​

Answer 1

Accurate Question :

If 2x -  3y is equals to 10 and xy is equals to 16. Find the value of 8x³ -  27y³.

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

2x - 3y = 10........(1)

xy = 16.....(2)

★From (1) we get :-

2x = 10 + 3y

$\tt{\rightarrow x=\dfrac{10+3y}{2}.....(3)}$

${\boxed{\sf\:{Substitute\;value\;in\;Equation\;(2)}}}$

xy = 16

$\tt{\rightarrow\dfrac{10+3y}{2}\times y=16}$

y(10 + 3y) = 32

10y + 3y² = 32

3y² + 10y - 32 = 0

${\boxed{\sf\:{Splitting\;the\;middle\;Term}}}$

3y² - 6y + 16y - 32 = 0

3y(y - 2) + 16(y - 2)

(y - 2) (3y + 16)

y - 2 = 0

y = 2

3y + 16 = 0

3y = -16

$\tt{\rightarrow y=\dfrac{-16}{3}}$

= -8 (This is not applicable)

${\boxed{\sf\:{Hence\;we\;put}}}$

y = 2 (In Equation 3)

$\tt{\rightarrow x=\dfrac{10+3y}{2}}$

$\tt{\rightarrow 10+3\times\dfrac{2}{2}}$

= 13

${\boxed{\sf\:{Hence\;we\;get}}}$

8x³ - 27y

= 8 × (13)³ - 27 × 2

= 8 × 39 - 54

= 312 - 39

= 273

Answer 2

Answer:

The value of 8x³ - 27y³ = 273.

Step-by-step explanation:

The Accurate Question :

If 2x -  3y is equals to 10 and xy is equals to 16. Find the value of 8x³ -  27y³.

Solution :

Given that :

• 2x - 3y =  10
• xy = 16

To Find :

The value of 8x³ -  27y³.

Method :

From Question, We have :

$\sf \\\implies 2x-3y = 10\quad........Eq(1)\\ \\\implies xy = 16\quad.......E(2)\\ \\\implies 2x -3y = 10\\ \\\implies 2x = 10+3y\\ \\\implies x =\dfrac{10+3y}{2}\quad......(3)$

Now,

Using the value of x in Eq(2) :

$\sf\\ \implies xy= 16\\ \\\implies (10+\dfrac{3y}{2}) \times y = 16\\ \\\implies y(10+3y) = 32\\ \\\implies 10y + 3y^2 = 32$

$\sf\\\implies 3y^2+10y -32 = 0\\ \\\implies 3y^2 - 6y + 16y - 32 = 0\\ \\\implies 3y(y-2) + 16(y-2)\\ \\\implies (y-2) ( 3y+16)\\ \\\implies y -2 = 0\; and\; 3y +16 = 0\\ \\\implies y = 2\;and\; 3y = -16\\ \\\implies y = 2\;and\; y = \dfrac{-16}{3}\\ \\\implies x = \dfrac{10+3y}{2} = 10+ 3 \times \dfrac{2}{2} = 13\\ \\\implies 8x^3 - 27y =\\ \\\implies 8 \times (13)^3 - 27 \times 2\\ \\\implies 8 \times 39 - 54 = 312 - 39 = 273$

Hence,

The value of 8x³ - 27y³ = 273.