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प्रश्न
If `x + (1)/x = "p", x - (1)/x = "q"`; find the relation between p and q.
उत्तर
`x + (1)/x = "p", x - (1)/x = "q"`
`(x + 1/x)^2`
= `x^2 + (1)/x^2 +2`
⇒ p2 = `x^2 + (1)/x^2 + 2`
⇒ `x^2 + (1)/x^2 = "p"^2 - 2` ...(1)
Also, `(x - 1/x)^2`
= `x^2 + (1)/x^2 - 2`
⇒ `"q"^2 = x^2 + (1)/x^2 - 2`
⇒ `x^2 + (1)/x^2 = "q"^2 + 2` ...(2)
Equating the value `x^2 + (1)/x^2` from and (2), we get :
p2 - 2 = q2 + 2
⇒ p2 - q2 = 4.
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