Question

8x^3+27y^3 if 2x+3y=14 and xy=8

Answer 1

Concepts Used:-
1) Identity
${(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)$
2) Putting the values in an equation and solving for finding the required unknown value.

Answer 2

Answer:

8x³ + 27y³  =728

Step-by-step explanation:

Given,

2x+3y=14

xy = 8

To find,

The value of 8x³+27y³

Recall the  formula

(a+b)³ = a³+b³ + 3ab(a+b) --------------(1)

Solution:

Let us take a =  2x and b = 3y

Then a+b = 2x+3y

ab = 2x×3y = 6×xy

Since it is given that 2x+3y = 14 and xy = 8

we have

a+b = 2x+3y = 14

ab = 6×xy = 6×8 = 48

Substituting the values of a, b, a+b and ab in equation(1)

(14)³ = (2x)³+(3y)³ + 3×48×14

2744  = 8x³ + 27y³ + 2016

8x³ + 27y³  = 2744 - 2016

=728

∴ 8x³ + 27y³  =728

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