if 2x = 3y = 12 and xy = 6, find the value of 8x³ + 27y³ using substitution method
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Answer:
Question is wrong
It should be 2x+3y or 2x-3y
Step-by-step explanation:
I have assumed 2x+3y
Just you have to substitute the values of 2x+3y
or xy in the required equation using formula of cubes.
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METHOD 1 :
2x + 3y = 13 ……….(1)
Cubing both sides :
(2x + 3y)³ = 2197
Using (a + b)³ = a³ + b³ + 3 ab (a + b) ,
= > 8x³ + 27y³ + 3 × 2 x × 3 y (2 x + 3 y ) = 2197
From (1) we have :
= > 8x³ + 27y³ + 18 xy(13) = 2197
= > 8x³ + 27y³ + 18×6×13 = 2197
= > 8x³ + 27y³ + 1404 = 2197
= > 8x³ + 27y³ = 2197 - 1404
= > 8x³ + 27y³ = 793
METHOD 2 :
2x + 3y - 13 = 0
If a + b + c = 0 , a³ + b³ + c³ = 3 abc
= > 8x³ + 27y³ - 2197 = 3 × (-13) × 6 xy
= > 8x³ + 27y³ - 2197 = - 234 × 6
= > 8x³ + 27y³ = 2197 - 1404
= > 8x³ + 27y³ = 793
2.3K viewsView 11 Upvoters · Answer requested by Ruchi Chhabra
Related Questions (More Answers Below)
2x + 3y = 13 ……….(1)
Cubing both sides :
(2x + 3y)³ = 2197
Using (a + b)³ = a³ + b³ + 3 ab (a + b) ,
= > 8x³ + 27y³ + 3 × 2 x × 3 y (2 x + 3 y ) = 2197
From (1) we have :
= > 8x³ + 27y³ + 18 xy(13) = 2197
= > 8x³ + 27y³ + 18×6×13 = 2197
= > 8x³ + 27y³ + 1404 = 2197
= > 8x³ + 27y³ = 2197 - 1404
= > 8x³ + 27y³ = 793
METHOD 2 :
2x + 3y - 13 = 0
If a + b + c = 0 , a³ + b³ + c³ = 3 abc
= > 8x³ + 27y³ - 2197 = 3 × (-13) × 6 xy
= > 8x³ + 27y³ - 2197 = - 234 × 6
= > 8x³ + 27y³ = 2197 - 1404
= > 8x³ + 27y³ = 793
2.3K viewsView 11 Upvoters · Answer requested by Ruchi Chhabra
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