Question

If 7x-5y=6 and xy=9,then find the value of 343x^3-125^3.

Answer 1

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correct equation : 343x^3 - 125y^3
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Given , 7 x - 5 y = 6 , x y = 9

here, 7 x - 5 y = 6

on squaring both side we get

( 7 x - 5y )^2 = ( 6 )^2

49 x^2 + 25 y^2 - 70 x y = 36

49 x^2 + 25 y^2 - 70 (9 ) = 36

49 x^2 + 25 y^2 - 630 = 36

49 x^2 + 25 y^2 = 666 ( note )
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343 x^3 - 125 y^3

=( 7x )^3 - ( 5y )^3

use identiy :
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a^3 - b^3 = ( a - b ) ( a^2 + ab + b^2 )
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Here , we have a = 7x ,b = 5y

(7 x )^3 - (5 y )^3

=( 7x - 5y )[ ( 7x )^2 + (7x ) ( 5y ) + (5y)^2 ]

=( 7x - 5y) (49x^2 + 35xy + 25y^2 )

=(7x - 5y ) ( 49x^2 + 25y^2 + 35xy )

=6 ( 666 + 35( 9 ) )

=6 ( 666 + 315 )=6 × 981

=5886

therefore ,

343x^3 - 125y^3 = 5886
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Your Answer : 5886
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