Advertisements
Advertisements
प्रश्न
If `(x^2 + 1)/x = 3 1/3` and x > 1; find If `x^3 - 1/x^3`
If `(x^2 + 1)/x = 3 1/3 "find" x^3 - 1/x^3`
Advertisements
उत्तर
Given `(x^2 + 1)/x = 3 1/3`
`(x^2 + 1)/x = 10/3`
`x + 1/x = 10/3`
Squaring on both sides, we get
`(x + 1/x)^2 = (10/3)^2`
`x^2 + 1/x^2 + 2 = 100/9`
`x^2 + 1/x^2 = (100 - 18)/9`
`∴x^2 + 1/x^2 = 82/9`
Also,
`x - 1/x = sqrt((x+1/x)^2 - 4)`
= `sqrt(100/9 - 4)`
= `sqrt(64/9)`
∴ `x - 1/x = 8/3`
Cubing both sides, we get
`(x - 1/x)^3 = (8/3)^3`
`x^3 - 1/x^3 - 3(x - 1/x) = 512/27`
`x^3-1/x^3-3(8/3)=512/27`
`x^3 - 1/x^3 - 8 = 512/27`
`x^3 - 1/x^3 = 512/27 + 8`
`x^3 - 1/x^3 = (512 + 216)/27`
∴ `x^3 - 1/x^3 = 728/27`
Notes
Students should refer to the answer according to the question.
संबंधित प्रश्न
Expand : ( x + 8 ) ( x + 10 )
Expand : ( x - 8 )( x - 10 )
If a2 + b2 + c2 = 50 and ab + bc + ca = 47, find a + b + c.
If x + 2y + 3z = 0 and x3 + 4y3 + 9z3 = 18xyz ; evaluate :
`[( x + 2y )^2]/(xy) + [(2y + 3z)^2]/(yz) + [(3z + x)^2]/(zx)`
If a + `1/a` = m and a ≠ 0 ; find in terms of 'm'; the value of :
`a - 1/a`
In the expansion of (2x2 - 8) (x - 4)2; find the value of constant term.
If x2 + `x^(1/2)`= 7 and x ≠ 0; find the value of:
7x3 + 8x − `7/x^3 - 8/x`
If `(x^2 + 1)/x = 3 1/3` and x > 1; Find `x - 1/x`.
Find the value of 'a': 4x2 + ax + 9 = (2x + 3)2
If x = `1/( x - 5 ) "and x ≠ 5. Find" : x^2 - 1/x^2`
