Question

Q.5 Solve: xa+yb = a + b; xa2+yb2 =2, a, b = 0​

Answer 1

Answer:

Solution:-

a

x

+

b

y

=a+b⟶eq.(1)

a

2

x

+

b

2

y

=2⟶eq.(2)

By multiplying eq.(1)by

a

1

,we get

a

2

x

+

ab

y

=1+

a

b

⟶eq.(3)

On subtracting eq. (3)from(2), we get

a

2

x

+

b

2

y

−

a

2

x

−

ab

y

=2−1−

a

b

⇒

b

y

(

b

1

−

a

1

)=1−

a

b

⇒

b

y

=b

⇒y=b

2

On putting the value of y in eq. (1), we get

a

x

+

b

b

2

=a+b⇒x=a

2

Hence, x=a

2

&y=b

2

.