Grade 12th passAlgebra
Que .xxiiiPlzzzzzzzzzzz solve this mode inequality question............. .. ......................
Que .xxiii
Plzzzzzzzzzzz solve this mode inequality question
............. .. ......................
1 Answer
Aditya Gupta
this ques can be solved by using a neat “trick”.
basically, |a| is less than equal to 1 if and only if a^2 is less than equal to 1. this can be proved simply by noting that a^2 – 1= (|a| – 1)(|a|+1).
so we can square both sides in the given inequality.
we get (x^2 – 5x+4)^2/(x – 2)^2(x+2)^2 is less than equal to 1.
or (x^2 – 5x+4)^2/(x – 2)^2(x+2)^2 – 1 is less than equal to 0
or [(x^2 – 5x+4)^2 – (x^2 – 4)^2]/(x – 2)^2(x+2)^2 is less than equal to 0
factorise the numerator.
x(x – 5/2)(x – 8/5)/(x – 2)^2(x+2)^2 is greater than equal to 0.
by wavy curve method, we obtain the final ans as
x belongs to [0, 8/5] U [5/2, infinity).
kindly approve :)
Other Related Questions on algebra
How do you write “the product of 18 and q” as an algebraic expression?
How do you write “the product of 18 and q” as an algebraic expression?
algebra
Last Activity: 2 Years ago