Advertisements
Advertisements
प्रश्न
If \[x - \frac{1}{x} = - 1\] find the value of \[x^2 + \frac{1}{x^2}\]
Advertisements
उत्तर
In the given problem, we have to find `x^2 + 1/x^2`
Given `(x-1/x)=-1`
On squaring both sides we get,
`(x-1/x)^2=(-1)^2`
We shall use the identity `(x-y )^2 = x^2 - 2xy + y`
`x^2 +1/x^2 - 2 xx x xx 1/x =- 1 xx -1`
`x^2 +1/x^2 -2 =1`
`x^2 +1/x^2 = 1+2`
`x^2+1/x^2 =3`
Hence the value of ` x^2 +1/x^2`is 3 .
APPEARS IN
संबंधित प्रश्न
Factorise:
4x2 + 9y2 + 16z2 + 12xy – 24yz – 16xz
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 3x2 – 12x |
Simplify the expression:
`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`
Evaluate of the following:
1043 + 963
Simplify of the following:
(x+3)3 + (x−3)3
If a + b = 10 and ab = 16, find the value of a2 − ab + b2 and a2 + ab + b2
If a + b + c = 9 and ab +bc + ca = 26, find the value of a3 + b3+ c3 − 3abc
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] =
If \[x^2 + \frac{1}{x^2} = 102\], then \[x - \frac{1}{x}\] =
If a + b + c = 9 and ab + bc + ca =23, then a3 + b3 + c3 − 3abc =
Use the direct method to evaluate :
(0.5−2a) (0.5+2a)
Use the direct method to evaluate :
`("a"/2-"b"/3)("a"/2+"b"/3)`
Expand the following:
(3x + 4) (2x - 1)
Find the squares of the following:
9m - 2n
If p + q = 8 and p - q = 4, find:
p2 + q2
If `x^2 + (1)/x^2 = 18`; find : `x - (1)/x`
Expand the following:
`(1/x + y/3)^3`
Find the value of x3 + y3 – 12xy + 64, when x + y = – 4
