Advertisements
Advertisements
प्रश्न
If `x^4 + 1/x^4 = 194, "find" x^3 + 1/x^3`
Advertisements
उत्तर
In the given problem, we have to find the value of `x^3 + 1/x^3.`
Given: `x^4 + 1/x^4 = 194`
We know that,
`(x^2 + 1/x^2)^2 = x^4 + 1/x^4 + 2` ...[Using (a + b)2 = a2 + b2 + 2ab]
Now, substituting the given value
`(x^2 + 1/x^2)^2 = 194 + 2`
∴ `(x^2 + 1/x^2)^2 = 196`
∴ `x^2 + 1/x^2 = sqrt196`
∴ `x^2 + 1/x^2 = +-14`
Let’s relate it to `x^3 + 1/x^3`
`(x + 1/x)^2 = x^2 + 1/x^2 + 2` ...[Using (a + b)2 = a2 + b2 + 2ab]
`(x + 1/x)^2 = 14 + 2`
∴ `x + 1/x = sqrt16`
∴ `x + 1/x = +-sqrt4`
Thus,
`x^3 + 1/x^3 = (x + 1/x)^3 - 3(x + 1/x)`
`x^3 + 1/x^3 = (4)^3 - 3(4)`
`x^3 + 1/x^3 = 64 - 12`
∴ `x^3 + 1/x^3 = +-52`
संबंधित प्रश्न
Evaluate the following product without multiplying directly:
104 × 96
Factorise the following using appropriate identity:
`x^2 - y^2/100`
Write the following cube in expanded form:
(2x + 1)3
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
Find the cube of the following binomials expression :
\[\frac{1}{x} + \frac{y}{3}\]
Evaluate of the following:
`(10.4)^3`
Find the following product:
If a + b = 10 and ab = 16, find the value of a2 − ab + b2 and a2 + ab + b2
If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]
If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =
If a + b + c = 0, then \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab} =\]
If a + b = 7 and ab = 10; find a - b.
Use the direct method to evaluate :
(3b−1) (3b+1)
Expand the following:
(a + 4) (a + 7)
Find the squares of the following:
9m - 2n
Find the squares of the following:
(2a + 3b - 4c)
Evaluate the following without multiplying:
(999)2
If `"a" + 1/"a" = 6;`find `"a" - 1/"a"`
If x + y + z = p and xy + yz + zx = q; find x2 + y2 + z2.
Without actually calculating the cubes, find the value of:
(0.2)3 – (0.3)3 + (0.1)3
