If x = a + (1/a) and y = a - (1/a) then x4 + y4 - 2x2y2 = ?
Solution
Correct Answer: Option C
দেওয়া আছে,
x = a + 1/a
y = a - 1/a
x + y = a + (1/a) + a - (1/a) = 2a
x - y = a + (1/a) - a + (1/a) = 2/a
এখন,
x4 + y4 - 2x2y2 = (x2)2 + (y2)2 - 2.x2.y2
= (x2 - y2)2
= {(x + y)(x - y)}2
= {(2a)(2/a)}2
= 42
= 16
x = a + 1/a
y = a - 1/a
x + y = a + (1/a) + a - (1/a) = 2a
x - y = a + (1/a) - a + (1/a) = 2/a
এখন,
x4 + y4 - 2x2y2 = (x2)2 + (y2)2 - 2.x2.y2
= (x2 - y2)2
= {(x + y)(x - y)}2
= {(2a)(2/a)}2
= 42
= 16
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