Advertisements
Advertisements
Question
If `"a" - 1/"a" = 10;` find `"a" + 1/"a"`
Advertisements
Solution
`"a" - 1/"a" = 10`
`("a" - 1/"a")^2`
= `"a"^2 + 1/"a"^2 - 2("a") (1/"a")`
⇒ (10)2
= `"a"^2 + 1/"a"^2 - 2`
⇒ `"a"^2 + 1/"a"^2`
= 102
Now, `("a" + 1/"a"^2)`
= `"a"^2 + 1/"a"^2 + 2("a") (1/"a")`
= 102 + 2
= 104
⇒ `"a"^2 - 1/"a"^2`
= `sqrt(104)`
= ±2`sqrt(26)`.
APPEARS IN
RELATED QUESTIONS
Find the cube of the following binomials expression :
\[4 - \frac{1}{3x}\]
If \[x - \frac{1}{x} = 5\], find the value of \[x^3 - \frac{1}{x^3}\]
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
If 49a2 − b = \[\left( 7a + \frac{1}{2} \right) \left( 7a - \frac{1}{2} \right)\] then the value of b is
If a2 - 5a - 1 = 0 and a ≠ 0 ; find:
- `a - 1/a`
- `a + 1/a`
- `a^2 - 1/a^2`
Use the direct method to evaluate :
(3b−1) (3b+1)
Expand the following:
`(2"a" + 1/(2"a"))^2`
If x + y = 1 and xy = -12; find:
x - y
If a2 + b2 + c2 = 41 and a + b + c = 9; find ab + bc + ca.
