Advertisements
Advertisements
Question
If `x^2 + 1/x^2 = 66`, find the value of `x - 1/x`
Solution
`(x - 1/x)^2 = x^2 = 1/x^2 - 2 xx x xx 1/x`
`(x - 1/x)^2 = x^2 + 1/x^2 - 2`
`=>(x - 1/x)^2 = 66 - 2` [∵ `x^2 + 1/x^2 = 66`]
`=> (x - 1/x)^2 = 64`
`=> (x - 1/x)^2 = (+-8)^2`
`=> x - 1/x = +-8^2`
APPEARS IN
RELATED QUESTIONS
Use suitable identity to find the following product:
(x + 8) (x – 10)
Use suitable identity to find the following product:
`(y^2+3/2)(y^2-3/2)`
Factorise the following:
64a3 – 27b3 – 144a2b + 108ab2
Evaluate the following using identities:
(2x + y) (2x − y)
Evaluate the following using identities:
117 x 83
If 2x+3y = 13 and xy = 6, find the value of 8x3 + 27y3
If \[x + \frac{1}{x} = 3\], calculate \[x^2 + \frac{1}{x^2}, x^3 + \frac{1}{x^3}\] and \[x^4 + \frac{1}{x^4}\]
If a − b = 5 and ab = 12, find the value of a2 + b2
Find the square of 2a + b.
If a - b = 4 and a + b = 6; find
(i) a2 + b2
(ii) ab
Use the direct method to evaluate :
(ab+x2) (ab−x2)
Simplify by using formula :
(5x - 9) (5x + 9)
If x + y = 9, xy = 20
find: x2 - y2.
If `x^2 + (1)/x^2 = 18`; find : `x - (1)/x`
If `"r" - (1)/"r" = 4`; find : `"r"^4 + (1)/"r"^4`
Simplify:
`(x - 1/x)(x^2 + 1 + 1/x^2)`
Which one of the following is a polynomial?
Prove that (a + b + c)3 – a3 – b3 – c3 = 3(a + b)(b + c)(c + a).
