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Question-188375




Question Number 188375 by Rupesh123 last updated on 28/Feb/23
Commented by Frix last updated on 28/Feb/23
M=45 at x=−((17)/2)
$${M}=\mathrm{45}\:\mathrm{at}\:{x}=−\frac{\mathrm{17}}{\mathrm{2}} \\ $$
Commented by Rupesh123 last updated on 28/Feb/23
Correct, sir!
Answered by qaz last updated on 28/Feb/23
∣a^→ ∣+∣b^→ ∣≥∣a^→ +b^→ ∣    ,a^→ =(x+16,10)  b^→ =(11−x,26)  ⇒(√((x+16)^2 +10^2 ))+(√((x−11)^2 +26^2 ))≥∣(27,36)∣=(√(27^2 +36^2 ))=45
$$\mid\overset{\rightarrow} {{a}}\mid+\mid\overset{\rightarrow} {{b}}\mid\geqslant\mid\overset{\rightarrow} {{a}}+\overset{\rightarrow} {{b}}\mid\:\:\:\:,\overset{\rightarrow} {{a}}=\left({x}+\mathrm{16},\mathrm{10}\right)\:\:\overset{\rightarrow} {{b}}=\left(\mathrm{11}−{x},\mathrm{26}\right) \\ $$$$\Rightarrow\sqrt{\left({x}+\mathrm{16}\right)^{\mathrm{2}} +\mathrm{10}^{\mathrm{2}} }+\sqrt{\left({x}−\mathrm{11}\right)^{\mathrm{2}} +\mathrm{26}^{\mathrm{2}} }\geqslant\mid\left(\mathrm{27},\mathrm{36}\right)\mid=\sqrt{\mathrm{27}^{\mathrm{2}} +\mathrm{36}^{\mathrm{2}} }=\mathrm{45} \\ $$
Commented by Rupesh123 last updated on 28/Feb/23
Correct, sir!

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