1.

Find the value of x is​

Answer»

Topic :-

Linear Equations

Given :-

\dfrac{<klux>X</klux>+b}{a-b}=\dfrac{x-b}{a+b}

To FIND :-

Value of 'x'.

Solution :-

Cross Multiply,

( x + b )( a + b ) = ( x - b )( a - b )

Simplify it,

x( a + b ) + b( a + b ) = x( a - b ) - b( a - b )

ax + bx + ab + b² = ax - bx - ab + b²

Canceling few terms,

ax - ax + b² - b² + bx + ab = - bx - ab

0 + 0 + bx + ab = - bx - ab

bx + ab = - bx - ab

Group similar kind of terms,

bx + bx = - ab - ab

2bx = - 2ab

Divide by 2 both sides,

bx = - ab

bx + ab = 0

b( x + a ) = 0

So,

EITHER b = 0 or

x + a = 0 which gives

x = - a

Answer :-

So, value of x is -a.

Verification :-

\dfrac{x+b}{a-b}=\dfrac{x-b}{a+b}

Put x = -a in LEFT HAND Side ( LHS),

\dfrac{-a+b}{a-b}=-1

Put x = -a in Right Hand Side ( RHS),

\dfrac{-a-b}{a+b}=-1

We observe that LHS = RHS.

Hence, verified !


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