Advertisements
Advertisements
प्रश्न
If `x + (1)/x = "p", x - (1)/x = "q"`; find the relation between p and q.
Advertisements
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.
APPEARS IN
संबंधित प्रश्न
Factorise the following:
27y3 + 125z3
Give possible expression for the length and breadth of the following rectangle, in which their area are given:
| Area : 25a2 – 35a + 12 |
Write in the expand form: `(2x - y + z)^2`
Evaluate of the following:
(9.9)3
Find the following product:
\[\left( \frac{3}{x} - \frac{5}{y} \right) \left( \frac{9}{x^2} + \frac{25}{y^2} + \frac{15}{xy} \right)\]
Find the following product:
If \[\frac{a}{b} + \frac{b}{a} = 1\] then a3 + b3 =
If a2 - 5a - 1 = 0 and a ≠ 0 ; find:
- `a - 1/a`
- `a + 1/a`
- `a^2 - 1/a^2`
Find the squares of the following:
9m - 2n
Factorise the following:
9x2 + 4y2 + 16z2 + 12xy – 16yz – 24xz
