Question : If $(x+y)^2=xy+1$ and $x^3-y^3=1$, what is the value of $(x-y)$?
Option 1: 1
Option 2: 0
Option 3: –1
Option 4: 2
Answer (1)
23rd Jan, 2024
Correct Answer: 1
Solution :
Given:
$(x+y)^2=xy+1$ and $x^3-y^3=1$
Consider, $(x+y)^2=xy+1$
⇒ $x^2+y^2+2xy-xy=1$
⇒ $x^2+y^2+xy=1$
Now, we know, $x^3-y^3=(x-y)(x^2+xy+y^2)$
⇒ $1=(x-y)×1$
$\therefore(x-y)=1$
Hence, the correct answer is 1.
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