find the value of 27x^3+8y^3 if 3x+2y=7 and xy=2
Answers
Answered by
9
Given:-
- 27x³ + 8y³
- 3x + 2y = 7
- xy = 2
Solution :-
=> 27x³ + 8y³
= (3x)³ + (2y)³
= (3x + 2y) [ (3x)² - (3x × 2y) + (2y)² ]
{ ∵ (a + b) (a² - ab + b²}
= 7 [ (3x)² - 6(xy) + (2y)² ]
= 7 [ (3x + 2y)² - 12xy - 6xy]
= 7 [ (7)² - 18xy ]
= 7[49 - 18(2)]... { given⇒ xy = 2 }
= 7(49 - 36)
= 7×13
= 91
Answered by
1
Answer:
Given:-
27x³ + 8y³
3x + 2y = 7
xy = 2
Solution :-
=> 27x³ + 8y³
= (3x)³ + (2y)³
= (3x + 2y) [ (3x)² - (3x × 2y) + (2y)² ]
{ ∵ (a + b) (a² - ab + b²}
= 7 [ (3x)² - 6(xy) + (2y)² ]
= 7 [ (3x + 2y)² - 12xy - 6xy]
= 7 [ (7)² - 18xy ]
= 7[49 - 18(2)]... { given⇒ xy = 2 }
= 7(49 - 36)
= 7×13
= 91
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