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sergiy2304 [10]

2 years ago

12

Given m * n denotes 2m + n, evaluate:

1 answer:

mrs_skeptik [129]2 years ago

7 0

Answer:3.76.-9

Step-by-step explanation:

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<img src="https://tex.z-dn.net/?f=%20%7B%28%20%5Csqrt%7B3%7D%20%29%7D%5E%7Bx%20%2B%20y%7D%20%20%3D%209%20%5C%5C%20%20%7B%28%20%5

algol13

<h2> $\bf \purple{ \underline{Given :-}}$ </h2>

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

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

$\\$

<h2> $\bf \purple{ \underline{To \: Find :- }}$ </h2>

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

$\\$

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

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

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

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

$⇒ x + y = 4 \: \: \: \: (iii)$

$\\$

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

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

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

$⇒x - y = 10 \: \: \: \: (iv)$

$\\$

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

$x + y + x - y = 4 + 10$

$⇒2x = 14$

$⇒x = 7$

$\\$

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

$x - y - x - y = 10 - 4$

$⇒ - 2y = 6$

$⇒y = - 3$

$\\$

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

$\\$

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

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

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

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

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

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3 years ago

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