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
Use suitable identity to find the following product:
(3x + 4) (3x – 5)
Verify:
x3 + y3 = (x + y) (x2 – xy + y2)
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
Write in the expand form: `(2x - y + z)^2`
If \[x^2 + \frac{1}{x^2}\], find the value of \[x^3 - \frac{1}{x^3}\]
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
Use identities to evaluate : (97)2
Use the direct method to evaluate the following products :
(8 – b) (3 + b)
Use the direct method to evaluate :
(ab+x2) (ab−x2)
Expand the following:
(m + 8) (m - 7)
