Question

if 2 X + 3 Y is equal to 12 and X Y is equal to 6 find the value of 8 x cube + 27 y cube​

Answer 1

ACCORDING TO THE QUESTION....

2x+3y =12. 1⃣
xy = 6. 2⃣

now from 2⃣
x = 6/y

so by putting this in eq.1⃣
2(6/y)+3y = 12
12/y +3y =12
3(4/y+y ) =12
4/y +y = 12/3=4


$\frac{4}{y } + y = 4$
$y = 4 - \frac{4}{y}$
$y = \frac{4y - 4}{y}$
${y}^{2} = 4y - 4$
Now it is like a quadratic equation....
y² -4y + 4=0

By using splitting the middle term....
y² -2y -2y +4=0
y(y-2) -1(y-2) =0
(y-2)(y-1) =0

so y-2 = 0
[y = 2]

or y-1 =0
[y = 1]

Now by putting this value in eq.2⃣
If y = 2
so x×2 = 6
x= 6/2
[x = 3]

and if y = 1
so x×1 = 6
[x= 6]

$8 {x}^{3} + 27 {y}^{ 3}$
now to find this...
let x = 3 and y= 2

8(3)³ + 27(2)³
8(27) + 27(8)
216+216
432

now if we take x = 6 and y=1

8(6)³+ 27(1)³
8(216) +27
1728 +27
1755

hope this helps u....