Advertisements
Advertisements
प्रश्न
If x + \[\frac{1}{x}\] = then find the value of \[x^2 + \frac{1}{x^2}\].
Advertisements
उत्तर
We have to find the value of `x^2 + 1/x^2 `
Given `x+ 1/x = 3`
Using identity `(a+b)^2 = a^2 + 2ab + b^2`
Here `a= x,b= 1/x`
`(x+1/x)^2 = x^2 + 2 xx x xx 1/x + (1/x)^2`
`(x+1/x)^2 = x xx x +2 xx x xx 1/x + 1/x xx 1/x`
` (x+1/x)^2 = x^2 + 2+ 1/x^3`
By substituting the value of `x + 1/x = 3` we get,
`(3)^2 = x^2 + 2+ 1/x^2`
`3 xx 3 = x^2 + 2 +1/x^2`
By transposing + 2 to left hand side, we get
`9 -2 = x^2 +1/x^2`
`7 = x^2 + 1/x^2`
Hence the value of `x^2 + 1/x^2`is 7 .
APPEARS IN
संबंधित प्रश्न
Use suitable identity to find the following product:
(x + 8) (x – 10)
Factorise:
27x3 + y3 + z3 – 9xyz
Give possible expression for the length and breadth of the following rectangle, in which their area is given:
| Area : 35y2 + 13y – 12 |
Evaluate following using identities:
991 ☓ 1009
If `x^2 + 1/x^2 = 66`, find the value of `x - 1/x`
If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.
Simplify the following expressions:
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
Evaluate of the following:
(103)3
Find the following product:
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{3}{x} - \frac{x}{3} \right) \left( \frac{x^2}{9} + \frac{9}{x^2} + 1 \right)\]
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If \[x^4 + \frac{1}{x^4} = 194,\] then \[x^3 + \frac{1}{x^3} =\]
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
\[\frac{( a^2 - b^2 )^3 + ( b^2 - c^2 )^3 + ( c^2 - a^2 )^3}{(a - b )^3 + (b - c )^3 + (c - a )^3} =\]
The product (x2−1) (x4 + x2 + 1) is equal to
Use the direct method to evaluate :
`("a"/2-"b"/3)("a"/2+"b"/3)`
Find the squares of the following:
`(7x)/(9y) - (9y)/(7x)`
If `"a" - 1/"a" = 10`; find `"a"^2 - 1/"a"^2`
If `x + (1)/x = 3`; find `x^2 + (1)/x^2`
Simplify (2x – 5y)3 – (2x + 5y)3.
