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
Evaluate the following product without multiplying directly:
95 × 96
Expand the following, using suitable identity:
(2x – y + z)2
If 9x2 + 25y2 = 181 and xy = −6, find the value of 3x + 5y
If \[x^2 + \frac{1}{x^2}\], find the value of \[x^3 - \frac{1}{x^3}\]
If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If a - `1/a`= 8 and a ≠ 0 find :
(i) `a + 1/a (ii) a^2 - 1/a^2`
Use the direct method to evaluate the following products :
(8 – b) (3 + b)
Evaluate: (5xy − 7) (7xy + 9)
Evaluate the following without multiplying:
(999)2
