Advertisements
Advertisements
Question
If \[x^2 + \frac{1}{x^2} = 102\], then \[x - \frac{1}{x}\] =
Options
8
10
12
13
Advertisements
Solution
In the given problem, we have to find the value of `x- 1/x`
Given `x^2 + 1/x^2 = 102`
We shall use the identity `(a-b)^2 = a^2 + b^2 - 2ab`
Here putting`x^2 + 1/x^2 = 102`,
`(x-1/x)^2 = x^2 + 1/x^2 - 2 (x- 1/x)`
`(x-1/x)^2 =102 - 2(x xx 1/x)`
`(x- 1/x)^2 = 102 -2`
`(x- 1/x)^2 = 100`
`(x-1/x) xx (x - 1/ x) = 10 xx 10`
`(x-1/x) = 10`
Hence the value of `x-1/x`is 10 .
APPEARS IN
RELATED QUESTIONS
Factorise the following using appropriate identity:
`x^2 - y^2/100`
If x + y + z = 0, show that x3 + y3 + z3 = 3xyz.
Without actually calculating the cubes, find the value of the following:
(28)3 + (–15)3 + (–13)3
Evaluate of the following:
1113 − 893
Find the following product:
(7p4 + q) (49p8 − 7p4q + q2)
If a + b = 10 and ab = 16, find the value of a2 − ab + b2 and a2 + ab + b2
If \[x + \frac{1}{x}\] 4, then \[x^4 + \frac{1}{x^4} =\]
If a + b + c = 9 and ab + bc + ca =23, then a3 + b3 + c3 − 3abc =
Find the square of : 3a + 7b
Use identities to evaluate : (998)2
Use the direct method to evaluate :
(x+1) (x−1)
Use the direct method to evaluate :
(4+5x) (4−5x)
Simplify by using formula :
(5x - 9) (5x + 9)
If m - n = 0.9 and mn = 0.36, find:
m2 - n2.
If x + y = 1 and xy = -12; find:
x - y
If x + y = 1 and xy = -12; find:
x2 - y2.
If `x^2 + (1)/x^2 = 18`; find : `x - (1)/x`
Simplify:
(x + y - z)2 + (x - y + z)2
Using suitable identity, evaluate the following:
1033
Factorise the following:
16x2 + 4y2 + 9z2 – 16xy – 12yz + 24xz
