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STD 11 - 9. straight line — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 9. straight line1 Mark
MCQ
Let the expression $E = 8^a + 8^b -3.2^{a+b}$ takes its minimum value $'p'$ at $a = \alpha$ & $b = \beta $, then perpendicular distance of the point $P(\alpha , \beta )$ from the line $x + y + 2p = 0$ is
  • A
    $1$
  • B
    $0$
  • C
    $\frac{1}{{\sqrt 2 }}$
  • ✓
    $\sqrt 2 $
✓

Answer

Correct option: D.
$\sqrt 2 $
d
$\mathrm{E}+1=\left(2^{\mathrm{a}}\right)^{3}+(2 \mathrm{b})^{3}+1-3 \cdot 2^{\mathrm{a}} \cdot 2^{\mathrm{b}} \cdot 1$

$\mathrm{E}_{\min }=\mathrm{p}=-1 ; 2^{\mathrm{a}}=2^{\mathrm{b}}=1 \quad \Rightarrow \quad \mathrm{a}=\mathrm{b}=0$

$L = \sqrt 2 $

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