Question

If (x + y)2 = xy + 1 and x3 – y3 = 1, then what is the value of x – y?

A) 1 B) 0 C) -1 D) 2

Answer 1

Answer:

x + y = 1

Squaring on both sides,

x²+y²+2xy = 1

x²+y² = 1 - 2xy    ....... (1)

x³+y³ = 19

(x+y)(x²+y²-xy) =19

x²+y²-xy =19     [Since x + y = 1]

x²+y² =19 + xy       .................(2)

From the equations (1) and (2)

1 - 2xy = 19 + xy

3xy = -18

xy = -6

Now, substitute the value of xy in equation (2)

x²+y² =19 + (-6) = 13

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