Question

If,
A + B =AB=A^2=B^2
Then,find the value of A and B
​

Answer 1

Answer:

$\huge\boxed{\mathsf{a=b=2}}$

Step-by-step explanation:

We are given an equality here :-

a + b = ab = a² = b² .

First let us look into this equation :-

a + b = a²

Transpose a to the other side :-

⇒ b = a² - a

Take a as common in the right hand side :-

⇒ b = a ( a - 1 )  ..........( 1 )

Note the equation now :-

a + b = ab

Transpose b to the right hand side :-

⇒ b = ab - a

Take a as common in the right hand side :-

⇒ b = a ( b - 1 ) ..........( 2 )

From (1) and (2) we get :-

a ( b - 1 ) = a ( a - 1 )

Cancel a both sides :-

⇒ b - 1 = a - 1

⇒ b = a

Hence a = b and now we can put all the values of b as a in the equation :-

a + b = ab

Put b = a :-

⇒ a + a = a × a

⇒ 2 a = a²

Cancel a both sides :-

⇒ a = 2

Hence the value of a is 2 .

Since b = a , the value of b is also 2 .

Answer 2

A^2 = B^2

A = B

A + B = AB

B + B = AB

2B = AB

2 = A

Since A = B, value of B is 2