# Find the Real Value of X and Y, If ( 3 X − 2 I Y ) ( 2 + I ) 2 = 10 ( 1 + I ) - Mathematics

Find the real value of x and y, if

$(3x - 2iy)(2 + i )^2 = 10(1 + i)$

#### Solution

$\left( 3x - 2iy \right) \left( 2 + i \right)^2 = 10 \left( 1 + i \right)$

$\Rightarrow \left( 3x - 2iy \right)\left( 4 + i^2 + 4i \right) = 10\left( 1 + i \right)$

$\Rightarrow \left( 3x - 2iy \right)\left( 3 + 4i \right) = 10\left( 1 + i \right)$

$\Rightarrow 9x + 12xi - 6iy - 8 i^2 y = 10 + 10i$

$\Rightarrow 9x + 8y + i\left( 12x - 6y \right) = 10 + 10i$

$\text{Comparing both the sides:}$

$9x + 8y = 10 . . . . (1)$

$12x - 6y = 10$

$or, 6x - 3y = 5 . . . (2)$

$\text { Multiplying equation (1) by 3 and equation (2) by 8 },$

$27x + 24y = 30 . . . . (3)$

$48x - 24y = 40 . . . . (4)$

$\text {Adding equations (3) and (4):}$

$75x = 70$

$\therefore x = \frac{14}{15}$

$\text { Substituting the value of x in equation (1): }$

$9 \times \frac{14}{15} + 8y = 10$

$\Rightarrow \frac{126}{15} + 8y = 10$

$\Rightarrow 8y = 10 - \frac{126}{15}$

$\Rightarrow 8y = \frac{24}{15}$

$\Rightarrow y = \frac{1}{5}$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 13 Complex Numbers
Exercise 13.2 | Q 2.2 | Page 31