Advertisements
Advertisements
प्रश्न
If `x + 1/x = sqrt5`, find the value of `x^2 + 1/x^2` and `x^4 + 1/x^4`
Advertisements
उत्तर
We have
`(x + 1/x)^2 = x^2 + 1/x^2 + 2 xx x xx 1/x`
`=> (x + 1/x)^2 = x^2 + 1/x^2 + 2`
`=> (sqrt5)^2 = x^2 + 1/x^2 + 2` [∵ `x + 1/x = sqrt5`]
`=> 5 = x^2 + 1/x^2 + 2`
`=> x^2 + 1/x^2 = 3` ......(1)
Now `(x^2 + 1/x^2)^2 = x^4 + 1/x^4 + 2 xx x^2 xx 1/x^2`
`=> (x^2 + 1/x^2)^2 = x^4 + 1/x^4 + 2`
`=> 9 = x^2 + 1/x^4 + 2` [∵ `x^2 + 1/x^2 = 3`]
`=> x^4 + 1/x^4 = 7`
Hence `x^2 + 1/x^2 = 3; x^4 + 1/x^4 = 7`
APPEARS IN
संबंधित प्रश्न
Expand the following, using suitable identity:
(–2x + 5y – 3z)2
Evaluate the following using identities:
(1.5x2 − 0.3y2) (1.5x2 + 0.3y2)
Write in the expanded form:
`(a + 2b + c)^2`
If a − b = 4 and ab = 21, find the value of a3 −b3
If \[x^2 + \frac{1}{x^2}\], find the value of \[x^3 - \frac{1}{x^3}\]
Evaluate of the following:
(9.9)3
If a + b + c = 9 and ab +bc + ca = 26, find the value of a3 + b3+ c3 − 3abc
\[\frac{( a^2 - b^2 )^3 + ( b^2 - c^2 )^3 + ( c^2 - a^2 )^3}{(a - b )^3 + (b - c )^3 + (c - a )^3} =\]
If 49a2 − b = \[\left( 7a + \frac{1}{2} \right) \left( 7a - \frac{1}{2} \right)\] then the value of b is
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
Use the direct method to evaluate :
(3b−1) (3b+1)
Use the direct method to evaluate :
(4+5x) (4−5x)
Simplify by using formula :
(1 + a) (1 - a) (1 + a2)
Evaluate the following without multiplying:
(95)2
If p + q = 8 and p - q = 4, find:
pq
If x + y + z = 12 and xy + yz + zx = 27; find x2 + y2 + z2.
If a2 + b2 + c2 = 41 and a + b + c = 9; find ab + bc + ca.
If `"a" + (1)/"a" = 2`, then show that `"a"^2 + (1)/"a"^2 = "a"^3 + (1)/"a"^3 = "a"^4 + (1)/"a"^4`
Find the following product:
`(x/2 + 2y)(x^2/4 - xy + 4y^2)`
