All real set of values of x satisfying x2-3x-+2>0 and x2- 2x-4 <=0 are given by [a,b)union (c,d] then value of b-a/d-c =
Answers
Given info : All real set of values of x satisfying x² - 3x + 2 > 0 and x² - 2x - 4 ≤ 0 are given by [a, b) U (c , d]
To find : the value of (b - a)/(d - c)
solution : case 1 : x² - 3x + 2 > 0
⇒x² - x - 2x + 2 > 0
⇒x(x - 1) - 2(x - 1) > 0
⇒(x - 2)(x - 1) > 0
⇒x > 2 or, x < 1 ........(1)
case 2 : x² - 2x - 4 ≤ 0
⇒x² - 2x + 1 - 1 - 4 ≤ 0
⇒(x - 1)² - 5 ≤ 0
⇒(x - 1)² - (√5)² ≤ 0
⇒[(x - 1) - √5)][(x - 1) + √5] ≤ 0
⇒1 - √5 ≤ x ≤ 1 + √5 .......(2)
find common set of values of equations (1) and (2)
we get, x ∈ [1 - √5, 1) U (2, 1 + √5]
therefore, a = 1 - √5 , b = 1
c = 2 , d = 1 + √5
now, (b - a)/(d - c) = (1 - 1 + √5)/(1 + √5 - 2)
= (√5)/(√5 - 1)
= (√5)(√5 + 1)/(√5² - 1²)
= (5 + √5)/4
Therefore the value of (b - a)/(d - c) is (5 + √5)/4
Answer:
that's it the answers is not the blunder as seen above which was provided before. I am writing this as this has to be a min of 20 characters.
