Question

please help me with this​

Answer 1

GIVEN :–

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

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

TO FIND :–

• To find the Value of 2x + y = ?

SOLUTION :–

• According to the first condition –

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

• We should write this as –

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

$\\ \implies \bf x + y = 4$

$\\ \implies \bf y = 4-x \: \: \: \: \: - - - eq.(1)$

• According to the second condition –

$\\ \implies \bf {( \sqrt{3})}^{x - y} = 32$

• We should write this as –

$\\ \implies \bf {( \sqrt{3})}^{x - y} = {( \sqrt{2} )}^{10}$

$\\ \implies \bf x-y = 10$

• By using eq.(1) –

$\\ \implies \bf x-(4 - x) = 10$

$\\ \implies \bf x-4 + x = 10$

$\\ \implies \bf 2x-4=10$

$\\ \implies \bf 2x=14$

$\\ \implies \bf x=7$

• Again Using eq.(1) –

$\\ \implies \bf y = 4-x$

$\\ \implies \bf y = 4-7$

$\\ \implies \bf y =-3$

• Now let's find 2x+y –

$\\ \implies \bf 2x + y = 2(7) - 3 = 11$