Let x and y be real numbers such that . Then the value of 10(x – 3y) is: [2026]

Question

Let x and y be real numbers such that $50 (\frac{2 x}{1 + 3 i} - \frac{y}{1 - 2 i}) = 31 + 17 i, i = \sqrt{- 1}$ . Then the value of 10(x – 3y) is: [2026]

Smart Achievers · Accepted Answer

(4)

Given : $50 (\frac{2 x}{1 + 3 i} - \frac{y}{1 - 2 i}) = 31 + 17 i$

$\Rightarrow 50 (\frac{2 x (1 - 3 i)}{1 + 9} - \frac{y (1 + 2 i)}{5}) = 31 + 17 i$

$\Rightarrow 10 (x (1 - 3 i) - y (1 + 2 i) = 31 + 17 i$

$\Rightarrow 10 (x - y) + 10 i (- 3 x - 2 y) = 31 + 17 i$

On comparing real and imaginary parts, we get

$x - y = \frac{31}{10}$ ... (i)

$- 3 x - 2 y = \frac{17}{10}$ ... (ii)

Solving (i) & (ii), we get

$x = \frac{9}{10} and y = \frac{- 11}{5}$

Now, $10 (x - 3 y) = 10 (\frac{9}{10} - 3 (- \frac{11}{5}))$

= 9 + 66 = 75

Solution

Q.
Let x and y be real numbers such that $50 (\frac{2 x}{1 + 3 i} - \frac{y}{1 - 2 i}) = 31 + 17 i, i = \sqrt{- 1}$ . Then the value of 10(x – 3y) is: [2026]

1 20

2 31

3 35

4 75

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