x2 - 3x + 1 = 0 হলে (x2 - 1/x2) এর মান-
Solution
Correct Answer: Option B
দেওয়া আছে,
x2 - 3x + 1 = 0
বা, x2 + 1 = 3x
বা, {(x2 + 1)/x} = 3
বা, x + (1/x) = 3
{x + (1/x)}2 = {x + (1/x)}2 - 4.x.(1/x)
{x + (1/x)}2 = 32 - 4
{x + (1/x)}2 = 5
{x + (1/x)}2 = 5
∴ x - 1/x = √5
(x2 - 1/x2) = (x + 1/x)(x - 1/x)
= 3.√5
= 3√5
x2 - 3x + 1 = 0
বা, x2 + 1 = 3x
বা, {(x2 + 1)/x} = 3
বা, x + (1/x) = 3
{x + (1/x)}2 = {x + (1/x)}2 - 4.x.(1/x)
{x + (1/x)}2 = 32 - 4
{x + (1/x)}2 = 5
{x + (1/x)}2 = 5
∴ x - 1/x = √5
(x2 - 1/x2) = (x + 1/x)(x - 1/x)
= 3.√5
= 3√5
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