Divide the number 20 into two parts such that sum of their squares is minimum.

Q.9 Divide the number 20 into two parts such that sum of their squares is minimum.

Doubtly Asked 28 Oct 2026 Board exam · March 2025 hsc 12th Save WhatsApp Report

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Answer: 10 and 10

Let the parts be \(x\) and \(20 - x\). Then \(S = x^2 + (20 - x)^2\).

\(\dfrac{dS}{dx} = 2x - 2(20 - x) = 4x - 40\). Setting \(\dfrac{dS}{dx} = 0\) gives \(x = 10\).

\(\dfrac{d^2S}{dx^2} = 4 \gt 0\), so \(S\) is minimum at \(x = 10\). The parts are 10 and 10 (minimum sum of squares \(= 200\)).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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