Question

Solve for x and y:

$\frac{bx}{a}+\frac{ay}{b}=a^2+b^2,x+y=2ab.$

Answer 1

( bx/a + ay/b = a^2 + b^2) ......... (1)

x + y = 2ab .... (2)

frm eq 1..

$(b^{2}x+a^{2}y)/ab=a2+b2$

$->b^{2}x+a^{2}y=a3b+b3a$

$->b^{2}x-b^{3}a=a^{3}b-a^{2}y$

$->b^2(x-ab)=a^2(ab-y)$

-> frm eq 2 ...
$b^2(x-x/2-y/2)=a^2(x/2+y/2-y)$

$->b^2(x/2-y/2)=a^2(x/2-y/2)$

$->b^{2}x-b^{2}y=a^{2}x-a^{2}y$

$->x(b^2-a^2)=y(b^2-a^2)$

$->x=y$

put the value of x in eq 2.... 2y = 2ab