Advertisements
Advertisements
प्रश्न
If \[x + \frac{1}{x}\] 4, then \[x^4 + \frac{1}{x^4} =\]
पर्याय
196
194
192
190
Advertisements
उत्तर
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
संबंधित प्रश्न
Without actually calculating the cubes, find the value of the following:
(28)3 + (–15)3 + (–13)3
Evaluate the following using identities:
(399)2
If `x + 1/x = sqrt5`, find the value of `x^2 + 1/x^2` and `x^4 + 1/x^4`
If 3x - 7y = 10 and xy = -1, find the value of `9x^2 + 49y^2`
Find the value of 4x2 + y2 + 25z2 + 4xy − 10yz − 20zx when x = 4, y = 3 and z = 2.
Evaluate of the following:
`(10.4)^3`
Simplify of the following:
\[\left( x + \frac{2}{x} \right)^3 + \left( x - \frac{2}{x} \right)^3\]
If a + b = 10 and ab = 16, find the value of a2 − ab + b2 and a2 + ab + b2
If x = −2 and y = 1, by using an identity find the value of the following
Find the following product:
(3x − 4y + 5z) (9x2 +16y2 + 25z2 + 12xy −15zx + 20yz)
Evaluate:
253 − 753 + 503
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If a − b = 5 and ab = 12, find the value of a2 + b2
Find the square of 2a + b.
Evaluate: (6 − 5xy) (6 + 5xy)
Simplify by using formula :
(5x - 9) (5x + 9)
If x + y = 1 and xy = -12; find:
x - y
Simplify:
(4x + 5y)2 + (4x - 5y)2
Expand the following:
(4a – b + 2c)2
