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
- A 30
- B 32
- C 34
- D 40
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 \(\mathrm{AM} \geq \mathrm{GM}\)…
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