If x = a + 1/a এবং y = a - 1/a হলে, x4 + y4 - 2x2y2=?
Solution
Correct Answer: Option C
দেওয়া আছে,
x = a + 1/a ......(i)
y = a - 1/a ...... (ii)
এখন,
(i)+(ii)⇒ x+y = 2a
(i)-(ii)⇒ x-y = 2/a
আবার,
x4 + y4 - 2x2y2
= (x2)2 - 2x2y2 + (y2)2
= ( x2 - y2)2
= {(x+y)(x-y)(x+y)(x-y)}
= (x+y)2 (x-y)2
= (2a)2 (2/a)2
= 4a2 . 4/a2
= 16
x = a + 1/a ......(i)
y = a - 1/a ...... (ii)
এখন,
(i)+(ii)⇒ x+y = 2a
(i)-(ii)⇒ x-y = 2/a
আবার,
x4 + y4 - 2x2y2
= (x2)2 - 2x2y2 + (y2)2
= ( x2 - y2)2
= {(x+y)(x-y)(x+y)(x-y)}
= (x+y)2 (x-y)2
= (2a)2 (2/a)2
= 4a2 . 4/a2
= 16
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