Question

a²×b²= a²+b²= ab² solve the equation​

Answer 1

a^2 × b^2 = a^2 + b^2 = ab^2

Consider a^2 × b^2 = ab^2.

a^2 × b^2 = ab^2

a^2 = a

a^2 - a = 0

a(a - 1) = 0

Therefore, a = 0 ; a = 1.

Consider a^2 × b^2 = a^2 + b^2.

a^2 × b^2 = a^2 + b^2

Taking a = 0,

0^2 × b^2 = 0^2 + b^2

0 × b^2 = 0^2 + b^2

0 = b^2

Therefore, b = 0.

Taking a = 1,

1^2 × b^2 = 1^2 + b^2

1 × b^2 = 1 + b^2

b^2 = b^2 + 1

b^2 - b^2 = 1

0 = 1

As a contradiction occurs here, a can't be 1.

Thus, a = b = 0.

Answer 2

Answer:

$a^{2} b^{2} =a^{2} + b^{2} =ab^{2} \\a^{2} b^{2} -ab^{2} =0  [tex][a^{2}-a] b^{2} =0 \\a[a-1]b^2 =0 \\a=0 or a=1 or b=0$

Step-by-step explanation:

case 1    a=0   then 0 = 0+b^2 =0    then b=0

case2    a=1   then b^2 = 1 + b^2  =b^2   then 1=0  impossible

case 3   b=0   then  0 = a^2 + 0 =0    then   a =0  

so        a=0 and b=0