Advertisements
Advertisements
Question
If \[x + \frac{1}{x}\] 4, then \[x^4 + \frac{1}{x^4} =\]
Options
196
194
192
190
Advertisements
Solution
In the given problem, we have to find the value of `x^4 + 1/x^4`
Given `x+ 1/x = 4`
We shall use the identity `(a+b)^2 = a^2 +b^2 + 2ab`
Here put,`x+ 1/x = 4`
`(x+ 1/x)^2 = x^2 + 1/x^2 + 2 (x xx 1/x)`
`(4)^2 = x^2 + 1/x^2 + 2 (x xx 1/x )`
`16 = x^2 + 1/x^2 + 2`
` 16 -2 = x^2 + 1/x^2`
`14 = x^2 + 1/x^2`
Squaring on both sides we get,
`(14)^2 = (x^2 + 1/x^2 )^2`
`14 xx 14 = (x^2)^2 + (1/x^2) ^2 + 2 xx x^2 xx 1/x^2`
`196 = x^4 + 1/x^4 + 2`
`196 -2 = x^4 + 1/x^4`
`194= x^4 + 1/x^4`
Hence the value of `x^4 + 1/x^4`is 194.
APPEARS IN
RELATED QUESTIONS
Factorise the following:
8a3 – b3 – 12a2b + 6ab2
Factorise the following:
`27p^3-1/216-9/2p^2+1/4p`
Factorise:
27x3 + y3 + z3 – 9xyz
Evaluate the following using identities:
(0.98)2
If `x + 1/x = sqrt5`, find the value of `x^2 + 1/x^2` and `x^4 + 1/x^4`
Write the expanded form:
`(-3x + y + z)^2`
Write in the expanded form:
`(m + 2n - 5p)^2`
Find the following product:
Find the following product:
If x = 3 and y = − 1, find the values of the following using in identify:
(9y2 − 4x2) (81y4 +36x2y2 + 16x4)
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{y} - \frac{y}{3} \right) \frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9}\]
If \[x^4 + \frac{1}{x^4} = 623\] then \[x + \frac{1}{x} =\]
\[\frac{( a^2 - b^2 )^3 + ( b^2 - c^2 )^3 + ( c^2 - a^2 )^3}{(a - b )^3 + (b - c )^3 + (c - a )^3} =\]
Evalute : `((2x)/7 - (7y)/4)^2`
Use the direct method to evaluate :
(0.5−2a) (0.5+2a)
If `x + (1)/x = 3`; find `x^4 + (1)/x^4`
If x + y = 1 and xy = -12; find:
x - y
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a" + (1)/"a"`
Which one of the following is a polynomial?
Using suitable identity, evaluate the following:
1033
