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bloodry

bloodry

13.02.2021 •

Mathematics

${( \sqrt{3} )}^{x + y} = 9 \\ {( \sqrt{2} )}^{x - y} = 32$ find the value of 2x + y.

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Ответ:

tylorroundy

13.02.2021

$\bf \purple{ \underline{Given :-}}$

$• \: {( \sqrt{3} )}^{x + y} = 9\: \: \: \: (i)$

$• \: {( \sqrt{2} )}^{x - y} = 32 \: \: \: \: (ii)$

$\\$

$\bf \purple{ \underline{To \: Find :- }}$

$• {\sf{The \: value \: of}} \: \: 2x+ y.$

$\\$

$\huge\bf \purple{ \underline{Solution :- }}$

$\sf{From \: equation \: (i), }$

${( \sqrt{3} )}^{x + y} = 9$

$⇒ {( \sqrt{3} )}^{x + y} = ({ \sqrt{3} })^{4}$

$⇒ x + y = 4 \: \: \: \: (iii)$

$\\$

$\sf{From \: the \: equation \: (ii)}$

${( \sqrt{2} )}^{x - y} = 32$

$⇒( { \sqrt{2} })^{x - y} =( { \sqrt{2} })^{10}$

$⇒x - y = 10 \: \: \: \: (iv)$

$\\$

$\sf{We \: have \: to \: add \: equation \: (iii) \: and \: equation \: (iv)}$

x + y + x - y = 4 + 10

⇒2x = 14

⇒x = 7

$\\$

$\sf{Subtracting \: equation \: (iii) \: from \: equation \: (ii), }$

x - y - x - y = 10 - 4

⇒ - 2y = 6

⇒y = - 3

$\\$

$\bf\therefore x = 7 \: \: and \: \: y = - 3$

$\\$

${ \sf{Th e \: value \: of }}= 2x +y$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =2 \times 7 + ( - 3)$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =14 - 3$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =11$

$\bf \red{Hence, \: the \: value \: of \: 2x + y \: is \: 11. }$

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Ответ:

justicejesusfreak

16.05.2021

It would be the one that says " 1:16 and 4:64 " because when you multiply 4 x 16 you would get 64. I hope de I helped you today

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