Let a2, a3 ∈ R be such that |a2-a3|=6 and f(x)=|1 a3 a2 1 a3 2 a2-x 1 2 a3-x a2|, x ∈ R. Then the greatest value of f(x) is

Question

Let a2, a3 ∈ R be such that |a2-a3|=6 and f(x)=|1 a3 a2 1 a3 2 a2-x 1 2 a3-x a2|, x ∈ R. Then the greatest value of f(x) is (A) 6 (B) 9 (C) 12 (D) 36

Tardigrade Admin · Accepted Answer

R2 arrow R2-R1 text and R3 arrow R3-R1 f(x)=-(a2-x)(a3-x)=-x2+(a2+a3) x-a2 a3 |a2-a3|=(√D/|a|)=6 ⇒ √D=6 text Max. =(-D/4 a)=(36/4)=9

Q. Let $a_{2}, a_{3} \in R$ be such that $∣ a_{2} - a_{3} ∣ = 6$ and $f (x) = ∣ ∣ 111 a_{3} a_{3} 2 a_{3} - x a_{2} 2 a_{2} - x a_{2} ∣ ∣, x \in R$ . Then the greatest value of $f (x)$ is