Question

if x/b+y/a=a/b ,bx-ay=ab then value of x^2+y^2​

Answer 1

Given -

$\frac{x}{b} + \frac{y}{a} = \frac{a}{b} \: and \: bx - ay = ab$

To find -

${x}^{2} + {y}^{2}$

Solution -

$\frac{x}{b} + \frac{y}{a} = \frac{a}{b}$

$\frac{ax + by}{ab} = \frac{a}{b}$

$ax + by = \frac{a}{b} \times ab$

$ax + by = {a}^{2} .......1)$

And,

$bx - ay = ab........2)$

Now,

1) ×a and 2)×b

Then the equations becomes

${a}^{2} x + aby = {a}^{3} .....3)$

And,

${b}^{2} x - aby = a {b}^{2} ....4)$

Now,

3) + 4)

${a}^{2} x + aby + {b}^{2} x - aby = {a}^{3} + a {b}^{2}$

${a}^{2} x + {b}^{2} x = {a}^{3} + a {b}^{2}$

$x( {a}^{2} + {b}^{2} ) = a( {a}^{2} + {b}^{2} )$

$x = a$

Putting the value of x in equation 1) we will get -

a×a+by=a²

a²+by=a²

by=0

y=0

Now,

=x²+y²

=a²+0

=a²

Therefore the value of x²+y² is a²