f x – y = 2 and xy = 15, find the value of : x^3 - y^3
Answers
Step-by-step explanation:
GIVEN :
there are given two equations
- x - y = 2 ---------1
2. x y = 15 ---------2
SOLUTION :
NOW FROM THE GIVEN TWO EQUATION, WE WILL FIND THE VALUE OF 'X' AND 'Y' BY SUBSTITUTION METHOD.
FROM EQUATION (2) we get ,
xy = 15
so, x = 15/y
putting the value of x=15/y in equation (1) we get,
x - y = 2
=》 15/y - y = 2
=》15/y - y²/y = 2
=》 15-y² = 2y ( hope you understand this step )
=》 2y + y² - 15 ( arrange in order)
=》 y² + 2y - 15
NOW SOLVING THE QUADRATIC EQUATION
=》 y² + 2y - 15 { (-15) = 5×(-3) }
=》 y² + 5y - 3y - 15
=》 y(y + 5) -3(y + 5)
=》 ● (y - 3) (y + 5)
HENCE WE GET 1. y - 3 = 0 =》 y = 3
2. y + 5 = 0 =》y = (-5) [ NEGLECTED ]
as, y = 3 so, xy = 15
x(3) = 15
so, x = 5
PUTTING VALUE OF x and y IN x³ - y³ , we get,
x³ - y³
=> (5)³ - (3)³
=> (125) - (27)
=> 125 - 27
=> 98
THEREFORE, OUR REQUIRED ANSWER IS 98..
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