Advertisements
Advertisements
Question
Mark the correct alternative in each of the following:
If \[x + \frac{1}{x} = 5\] then \[x^2 + \frac{1}{x^2} = \]
Options
25
10
23
27
Advertisements
Solution
In the given problem, we have to find the value of `x^2 + 1/x^2 `
Given `x+ 1/x = 5`
We shall use the identity `(a+b)^2 = a^2 + b^2 + 2ab`
Here put `x+1/x = 5`
`(x+1/x)^2 = x^2 +1/x^2 +2 (x xx 1/x)`
`(5)^2 = x^2 + 1/x^2 +2 (x xx 1/x)`
`25 = x^2 + 1/x^2 + 2`
`25 - 2 = x^2 +1/x^2`
`23 = x^2 + 1/x^2`
Hence the value of `x^2 + 1/x^2` is 23.
APPEARS IN
RELATED QUESTIONS
Write the following cube in expanded form:
`[3/2x+1]^3`
Evaluate the following using suitable identity:
(998)3
Factorise the following:
64a3 – 27b3 – 144a2b + 108ab2
Factorise the following:
64m3 – 343n3
if `x + 1/x = 11`, find the value of `x^2 + 1/x^2`
If 2x + 3y = 8 and xy = 2 find the value of `4x^2 + 9y^2`
Write in the expanded form:
(2a - 3b - c)2
Write in the expanded form: `(x + 2y + 4z)^2`
Write in the expand form: `(2x - y + z)^2`
Simplify the following expressions:
`(x^2 - x + 1)^2 - (x^2 + x + 1)^2`
If \[x^2 + \frac{1}{x^2} = 98\] ,find the value of \[x^3 + \frac{1}{x^3}\]
Evaluate of the following:
1113 − 893
Evaluate of the following:
463+343
Find the following product:
(2ab − 3b − 2c) (4a2 + 9b2 +4c2 + 6 ab − 6 bc + 4ca)
If a - b = 0.9 and ab = 0.36; find:
(i) a + b
(ii) a2 - b2.
Use the direct method to evaluate :
`(3/5"a"+1/2)(3/5"a"-1/2)`
Use the direct method to evaluate :
`("a"/2-"b"/3)("a"/2+"b"/3)`
Simplify:
(x + 2y + 3z)(x2 + 4y2 + 9z2 - 2xy - 6yz - 3zx)
If `49x^2 - b = (7x + 1/2)(7x - 1/2)`, then the value of b is ______.
Without actually calculating the cubes, find the value of:
`(1/2)^3 + (1/3)^3 - (5/6)^3`
