Advertisements
Advertisements
Question
If x + \[\frac{1}{x}\] = then find the value of \[x^2 + \frac{1}{x^2}\].
Advertisements
Solution
We have to find the value of `x^2 + 1/x^2 `
Given `x+ 1/x = 3`
Using identity `(a+b)^2 = a^2 + 2ab + b^2`
Here `a= x,b= 1/x`
`(x+1/x)^2 = x^2 + 2 xx x xx 1/x + (1/x)^2`
`(x+1/x)^2 = x xx x +2 xx x xx 1/x + 1/x xx 1/x`
` (x+1/x)^2 = x^2 + 2+ 1/x^3`
By substituting the value of `x + 1/x = 3` we get,
`(3)^2 = x^2 + 2+ 1/x^2`
`3 xx 3 = x^2 + 2 +1/x^2`
By transposing + 2 to left hand side, we get
`9 -2 = x^2 +1/x^2`
`7 = x^2 + 1/x^2`
Hence the value of `x^2 + 1/x^2`is 7 .
APPEARS IN
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
104 × 96
Verify:
x3 + y3 = (x + y) (x2 – xy + y2)
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
Evaluate the following using identities:
(2x + y) (2x − y)
Evaluate the following using identities:
(399)2
Write in the expanded form:
(2a - 3b - c)2
Evaluate of the following:
933 − 1073
Simplify of the following:
(2x − 5y)3 − (2x + 5y)3
Find the following product:
If x = −2 and y = 1, by using an identity find the value of the following
75 × 75 + 2 × 75 × 25 + 25 × 25 is equal to
If a + `1/a`= 6 and a ≠ 0 find :
(i) `a - 1/a (ii) a^2 - 1/a^2`
Use the direct method to evaluate the following products:
(x + 8)(x + 3)
Use the direct method to evaluate the following products :
(y + 5)(y – 3)
Use the direct method to evaluate :
(ab+x2) (ab−x2)
If `x + (1)/x = 3`; find `x^2 + (1)/x^2`
If p + q = 8 and p - q = 4, find:
pq
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" - (1)/"a"`
If `x/y + y/x = -1 (x, y ≠ 0)`, the value of x3 – y3 is ______.
Expand the following:
(4a – b + 2c)2
