Question

if 2x + 3y=13 and xy=6 then the value of 8x3+27y3 is-

(a)793 (b)2197

(c)1404 (d)none of these

Answer 1

Your answer !!

_____________________________

$2x + 3y = 13 , xy = 6 \\ \\ 8{x}^{3} + 27{y}^{3} \\ \\ {(2x)}^{3} + {(3y)}^{3} \\ \\ Using \: identity \\ \\ {(2x)}^{3} + {(3y)}^{3} + 3(2x)(3y)((2x+3y))\\ \\ 793$

Hence option A is correct ❗❗
____________________________

✌

Answer 2

Hey there! Thanks for the query!

Given, 2x + 3y = 13 and xy = 6

Cubing the both sides of the given equation.

( 2x + 3y ) = 13³

(2x)³ + (3y)³ + 3(2x)(3y)(2x + 3y ) = 2197

8x³ + 27y³ + 18xy ( 2x + 3y ) = 2197

8x³ + 27y³ + 18 ( 6 ) ( 13 ) = 2197

8x³ + 27y³ = 2197 - 1404

8x³ + 27y³ = 793

Therefore, The value of 8x³ + 27y³ = 793

Option A is the required answer of this question