Question

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

Answer 1

Step-by-step explanation:

Given:-

2x+3y= 12 and xy= 6

To find:-

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

Solution:-

Given that:

2x+3y= 12--------(1)

and xy= 6 -------(2)

On Cubing equation (1) : 2x+3y = 12 both sides

=>(2x+3y)^3 = 12^3

It is in the form of (a+b)^3

Where ,a = 2x

b=3y

we know that

(a+b)^3 = a^3 +3ab (a+b)+b^3

=>(2x)^3 + 3(2x)(3y)(2x+3y) + (3y)^2 = 12×12×12

=>8x^3 + 18xy(2x+3y) + 27y^3 = 1728

From (1)&(2) we have

2x+3y = 12 and xy=6

On Substituting this value in above

=>8x^3 +18(6)(12)+27y^3 = 1728

=>8x^3 + 1296 + 27y^3 = 1728

=>8x^3+27y^3 = 1728-1296

=>8x^3+27y^3 = 432

Therefore,8x^3+27y^3 = 432

Answer:-

The value of 8x³+27y³ for the given problem is 432

Used formula:-

• (a+b)^3 = a^3 +3ab (a+b)+b^3
• (a+b)^3 = a^3+3a^2b+3ab^2+b^3