Advertisements
Advertisements
Question
If `x^2 + 1/x^2 = 66`, find the value of `x - 1/x`
Advertisements
Solution
`(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`
`=>(x - 1/x)^2 = 66 - 2` [∵ `x^2 + 1/x^2 = 66`]
`=> (x - 1/x)^2 = 64`
`=> (x - 1/x)^2 = (+-8)^2`
`=> x - 1/x = +-8^2`
APPEARS IN
RELATED QUESTIONS
Verify:
x3 + y3 = (x + y) (x2 – xy + y2)
Simplify the expression:
`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`
If \[x^2 + \frac{1}{x^2} = 98\] ,find the value of \[x^3 + \frac{1}{x^3}\]
Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
Find the following product:
\[\left( \frac{3}{x} - \frac{5}{y} \right) \left( \frac{9}{x^2} + \frac{25}{y^2} + \frac{15}{xy} \right)\]
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
Evaluate:
253 − 753 + 503
If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =
Find the square of : 3a + 7b
Use the direct method to evaluate the following products :
(3x – 2y) (2x + y)
Use the direct method to evaluate :
(3b−1) (3b+1)
Find the squares of the following:
`(7x)/(9y) - (9y)/(7x)`
Simplify by using formula :
(x + y - 3) (x + y + 3)
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
If `x^2 + (1)/x^2 = 18`; find : `x - (1)/x`
If `"a" + (1)/"a" = 2`, then show that `"a"^2 + (1)/"a"^2 = "a"^3 + (1)/"a"^3 = "a"^4 + (1)/"a"^4`
Simplify:
(7a +5b)2 - (7a - 5b)2
Using suitable identity, evaluate the following:
9992
Find the value of x3 + y3 – 12xy + 64, when x + y = – 4
If a + b + c = 5 and ab + bc + ca = 10, then prove that a3 + b3 + c3 – 3abc = – 25.
