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
Factorize 4( x - y)2 -12( x - y)( x + y ) + 9(x + y )2
Factorize x2 - y2 - 4xz + 4z2
Factorize `9(2a - b)^2 - 4(2a - b) - 13`
8x3 + 27y3 - 216z3 + 108xyz
Evaluate: (6p2 - 8pq + 2q2) (- 5p)
The area of a rectangle is 6x2 – 4xy – 10y2 square unit and its length is 2x + 2y unit. Find its breadth.
Write in the form of an algebraic expression:
Perimeter (P) of a square is four times its side.
The value of 7a – 4b when a = 3, b = 2 is
Sonu and Raj have to collect different kinds of leaves for science project. They go to a park where Sonu collects 12 leaves and Raj collects x leaves. After some time Sonu loses 3 leaves and Raj collects 2x leaves. Write an algebraic expression to find the total number of leaves collected by both of them.
A school has a rectangular playground with length x and breadth y and a square lawn with side x as shown in the figure given below. What is the total perimeter of both of them combined together?
