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aman

· started a discussion

· 1 Months ago

189786.0 (Question: 189786.0 )

please explain again

Question:

If \(\cfrac{x}{y} + \cfrac{y}{x}\)  = -1, x, y \(\neq\) 0, then the value of 2(x3 –y3)  is –

Options:
A) 0
B) 1
C) -1 
D) 2
Solution:
Ans: (a)


shiv

· commented

· 1 Months ago

Rememer, If x+(1/x) = 1 then x cube = -1 and if x+(1/x) = -1 then x cube = +1
so, here: x cube = 1 and hence, (x cube) Minus 1/(x cube) = 1-1 = 0

Knowledge Expert

· commented

· 1 Months ago

Dear Student,

First of all simplify the equation: x/y+y/x = -1
X^2 + y^2 = -xy
X^2 + y^2 + xy = 0
Now, make multiplication of (x-y) both the sides,
(x-y)(X^2 + y^2 + xy) = 0*(x-y)
Since, x^3-y^3 = (x-y)(X^2 + y^2 + xy)
So, x^3-y^3 = 0
Now, make multiplication of 2 both the sides,
2(x^3-y^3) = 2*0
Hence, 2(x^3-y^3) = 0

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