Advertisements
Advertisements
प्रश्न
Factorize `[x^2 + 1/x^2] - 4[x + 1/x] + 6`
Advertisements
उत्तर
`= 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
संबंधित प्रश्न
Factorize the following expressions:
y3 +125
Factorize the following expressions:
a3 + 3a2b + 3ab2 + b3 - 8
(3x - 2 y)3 + (2 y - 4z )3 + (4z - 3x)3
What must be added to the following expression to make it a whole square?
4x2 − 20x + 20
If a + b + c = 9 and ab + bc + ca = 40, find a2 + b2 +c2.
Evaluate: (a2 + b2 + c2 - ab - bc - ca)(a + b + c)
Divide: m2 − 2mn + n2 by m − n
Divide: 9x2 - 24xy + 16y2 by 3x- 4y
Divide: 2m3n5 by - mn
The largest number of the three consecutive numbers is x + 1, then the smallest number is ________
