Question

a square upon x minus b square upon Y is equal to zero a square B upon x minus b square is equal to a + b

Answer 1

Answer:

The value of x and y are as follows:

x = a²(b-a)/(b+a)

y = b²(b-a)/(b+a)

Step-by-step explanation:

Given,

a²/x - b²/y = 0

=> a²/x =  b²/y

=> x = a²y/b²

also given that,

a²b/x - b²a/y = a + b

putting the value of x = a²y/b² in this equation we get,

b³/y - b²a/y = a + b

=> (b³ - b²a)/y = a + b

=> y = (b³ - b²a)/a + b

=> y = b²(b-a)/(b+a)

putting the value of y in the eqn  x = a²y/b²

=> x = a²/b² * b²(b-a)/(b+a)

=> x = a²(b-a)/(b+a)

Answer 2

Solution:

Let
$\frac{1}{x} = u \\ \\ \frac{1}{y} = v$
So, equation will become

${a}^{2} u - {b}^{2} v = 0 \: \: \: eq1 \\ \\ {a}^{2} bu - {b}^{2} av = a + b \: \: \: \: eq2$
multiply eq 1 by b and subtract from 2

${a}^{2} bu - {b}^{3} v = 0 \\ {a}^{2} bu - {b}^{2} av = a + b \\ - \: \: \: \: \: \: \: + \: \: \: \: \: \: \: \: \: \: - \: \: \: \: - \\ \\ {b}^{2} av - {b}^{3} v = - (a + b) \\ \\ {b}^{2} (a - b)v = - (a + b) \\ \\ v = \frac{a + b}{(b - a) {b}^{2} } \\ so \\ \\ y = \frac{(b - a) {b}^{2} }{a + b}$
put the value of y in eq 1 to get value of x

$\frac{ {a}^{2} }{x} - \frac{ {b}^{2} } {\frac{(b - a) {b}^{2} }{a + b}} = 0 \\ \\ \frac{ {a}^{2} }{x} - \frac{a + b}{(b - a)} = 0 \\ \\ \frac{ {a}^{2} }{x} = \frac{(a + b)}{(b - a)} \\ \\ x = \frac{(b - a) {a}^{2} }{(a + b)}$
Hope it helps you.