Let f(x) = |x – 2| and g(x) = |3 – x| and
A be the number of real solutions of the equation f(x) = g(x)
B be the minimum value of h(x) = f(x) + g(x)
C be the area of triangle formed by f(x) = |x – 2|, g(x) = |3 – x| and x-axis and α < γ < β < δ where α < β are the roots of f(x) = 4 and γ < δ are the roots of g(x) = 4, then the value of sum of digits of 
.
Text Solution
Verified by ExpertsD
f(x) = |x – 2|, g(x) = |x – 3|
f(x) = g(x) ⇒ |x – 2| 2 = |x – 3| 2 ⇒ x 2 – 4x + 4 = x 2 – 6x + 9
⇒ x = 
Hence A = 1
h(x) = |x – 2| + |x – 3| ≥ |(x – 2) – (x – 3)| = 1 ⇒ B = 1
hence C = 
|x – 2| = 4 ⇒ x = 2 ± 4 ⇒ α = –2 and β = 6
|x – 3| = 4 ⇒ x = 3 ± 4 ⇒ γ = –1 and δ = 7
= 4(4 + 36 + 1 + 49) = 360
Sum of digits = 9
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