Advertisements
Advertisements
Questions
If `(x^2 + 1)/x = 3 1/3` and x > 1; Find `x - 1/x`.
If `(x^2 + 1)/x = 3 1/3 "find" x - 1/x`.
Advertisements
Solution
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 = 100/9 - 2`
= `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`
RELATED QUESTIONS
If a2 + b2 + c2 = 35 and ab + bc + ca = 23; find a + b + c.
If a + b + c = p and ab + bc + ca = q ; find a2 + b2 + c2.
If x > 0 and `x^2 + 1/[9x^2] = 25/36, "Find" x^3 + 1/[27x^3]`
If 2( x2 + 1 ) = 5x, find :
(i) `x - 1/x`
(ii) `x^3 - 1/x^3`
If 2( x2 + 1 ) = 5x, find :
(i) `x - 1/x`
(ii) `x^3 - 1/x^3`
If a2 + b2 = 34 and ab = 12; find : 7(a - b)2 - 2(a + b)2
If x2 + `x^(1/2)`= 7 and x ≠ 0; find the value of:
7x3 + 8x − `7/x^3 - 8/x`
Find the value of 'a': 4x2 + ax + 9 = (2x - 3)2
If 3a + 5b + 4c = 0, show that : 27a3 + 125b3 + 64c3 = 180 abc
If x = `1/( x - 5 ) "and x ≠ 5. Find" : x^2 - 1/x^2`
