Advertisements
Advertisements
Question
if `x + 1/x = 11`, find the value of `x^2 + 1/x^2`
Advertisements
Solution
We have `x + 1/x = 11`
Now `(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`
`=> (11)^2 = x^2 + 1/x^2 + 2` [∵ `x = 1/x = 11`]
`=> 121 = x^2 = 1/x^2 + 2 `
`=> x^2 + 1/x^2 = 119`
APPEARS IN
RELATED QUESTIONS
Factorise:
4x2 + 9y2 + 16z2 + 12xy – 24yz – 16xz
Evaluate the following using suitable identity:
(99)3
Factorise the following:
64a3 – 27b3 – 144a2b + 108ab2
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
Evaluate following using identities:
991 ☓ 1009
Find the following product:
\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]
Find the following product:
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{y} - \frac{y}{3} \right) \frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9}\]
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If \[a^2 + \frac{1}{a^2} = 102\] , find the value of \[a - \frac{1}{a}\].
Evaluate: (2 − z) (15 − z)
Evaluate: (1.6x + 0.7y) (1.6x − 0.7y)
Expand the following:
(x - 3y - 2z)2
Evaluate, using (a + b)(a - b)= a2 - b2.
399 x 401
If m - n = 0.9 and mn = 0.36, find:
m2 - n2.
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
Simplify:
(7a +5b)2 - (7a - 5b)2
Which one of the following is a polynomial?
Expand the following:
(3a – 2b)3
Without actually calculating the cubes, find the value of:
(0.2)3 – (0.3)3 + (0.1)3
