ExamBro
ExamBro
AP EAMCET · Maths · Sequences and Series

\(a, b, c, d, e, f, g, h\) be distinct elements in the set \(\{-7,-5,-3,-2,2,4,6,13\}\). The minimum value of \((a+b+c+d)^2+(e+f+g+h)^2\) is

  1. A 30
  2. B 32
  3. C 34
  4. D 40
Verified Solution

Answer & Solution

Correct Answer

(B) 32

Step-by-step Solution

Detailed explanation

\[ \begin{aligned} & \text { Let } a+b+c+d=x \text { and } e+f+g+h=y \\ & x^2+y^2=(x+y)^2-2 x y \\ & =(13+6+4+2-2-3-5-7)^2-2 x y \\ & =64-2 x y \end{aligned} \] As we know \(\mathrm{AM} \geq \mathrm{GM}\)…