Question

Given (2 x + 3 y)2 = 169 and (2 x - 3 y)2 = 25. What is the value of xy ?​

Answer 1

Answer:

The value of x and y are $\frac{9}{2} \hspace {2mm} and \hspace {2mm} \frac{4}{3}$ Respectively.

Step-by-step explanation:

The algebraic expression given are

                   $(2 x + 3 y)^2 = 169\\ \\ (2 x + 3 y) = \sqrt{169} \\ \\ 2 x + 3 y=13----(1)\\ \\ \\ (2 x - 3 y)^2 = 25\\ \\ (2 x - 3 y) = \sqrt{25} \\ \\ 2x-3y=5----(2)$

Adding equation (1) and equation (2) , we get

                  $(2x+3y)+(2x-3y)=13+5\\ \\ 2x+2x+3y-3y=18\\ \\ 4x=18\\ \\ x=\frac{18}{4}\\ \\ x=\frac{9}{2}=4.5$

Putting the value of x in equation (1) , we get

                $2x+3y=13\\ \\ 2 \cdot (4.5)+3y=13\\ \\ 9+3y=13\\ \\ 3y=13-9\\ \\ 3y=4\\\\ y=\frac{4}{3}$