Advertisements
Advertisements
Question
Factorize `[x^2 + 1/x^2] - 4[x + 1/x] + 6`
Advertisements
Solution
`= x^2 + 1/x^2 - 4x - 4/x + 4 + 2`
`= x^2 + 1/x^2 + 4 + 2 - 4/x - 4x`
`= (x^2) + (1/x)^2 + (-2)^2 + 2 xx x xx x 1/x + 2x 1/x xx (-2) + 2(-2)x`
Using identity
a2 + b2 + c2 + 2ab + 2bc + 2ca = (a + b + c)2
We get
`= [x + 1/x + (-2)]^2`
`= [x + 1/x - 2]^2`
`= [x + 1/x - 2][x + 1/x - 2]`
`∴ [x^2 + 1/x^2] - 4[x + 1/x] + 6 = [x + 1/x - 2][x + 1/x - 2]`
APPEARS IN
RELATED QUESTIONS
8x3 + 27y3 - 216z3 + 108xyz
Find the value of the following expression: 81x2 + 16y2 − 72xy, when \[x = \frac{2}{3}\] and \[y = \frac{3}{4}\]
The factors of x3 − 7x + 6 are
Write the number of the term of the following polynomial.
5x2 + 3 x ax
Divide: 6x2 - xy - 35y2 by 2x - 5y
Express the following as an algebraic expression:
The product of 12, x, y and z minus the product of 5, m and n.
Solve the following equation.
3y + 4 = 5y − 6
Which of the following expressions has the value 37?
Write the variables, constant and terms of the following expression
29x + 13y
Shiv works in a mall and gets paid ₹ 50 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks.
