(লিখিত প্রশ্ন) If f(x,y) = (x² - 2xy + y²)/(x² - y²) then f(-x,-y) = ?
Solution
Correct Answer: Option A
দেওয়া আছে,
f(x,y) = (x² - 2xy + y²)/(x² - y²)
⇒ f(-x, -y) = {(-x)² - 2(-x)(-y) + (-y)²}/{(-x)² - (-y)²}
⇒ f(-x, -y) = (x² - 2xy + y²)/(x² - y²)
= (x - y)²/(x² - y²)
= {(x - y) (x - y)}/{(x - y)(x + y)}
= (x - y)/(x + y)
f(x,y) = (x² - 2xy + y²)/(x² - y²)
⇒ f(-x, -y) = {(-x)² - 2(-x)(-y) + (-y)²}/{(-x)² - (-y)²}
⇒ f(-x, -y) = (x² - 2xy + y²)/(x² - y²)
= (x - y)²/(x² - y²)
= {(x - y) (x - y)}/{(x - y)(x + y)}
= (x - y)/(x + y)
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