Question

A plus b ka whole square minus 4 a b x minus a minus b whole square is equal to zero

Answer 1

A plus b ka whole square minus 4 a b x minus a minus b whole square is equal to zero

Given,

(a+b)^2 - 4ab - (a-b)^2 = 0

we know the formulae

(a+b)^2 = a^2 + 2ab + b^2

(a-b)^2 = a^2 - 2ab + b^2

Now, we have,

LHS

= (a+b)^2 - 4ab - (a-b)^2

= (a^2 + 2ab + b^2) - 4ab - (a^2 - 2ab + b^2)

= a^2 + 2ab + b^2 - 4ab - a^2 + 2ab - b^2

= 4ab - 4ab

0 = 0 RHS

Hence proved that, LHS = RHS

Answer 2

The value of x in the given expression = 1

Step-by-step explanation:

The given expression:

$(a+b)^{2} -4abx-(a-b)^{2}=0$

To find, the value of x in the given expression.

∴ $(a+b)^{2} -4abx-(a-b)^{2}=0$

⇒ $[(a+b)^{2}-(a-b)^{2}] -4abx=0$

Using the algebraic identity,

$(a+b)^{2}-(a-b)^{2}=4ab$

⇒ 4ab - 4abx = 0

⇒ 4abx = 4ab

⇒ x = $\dfrac{4ab}{4ab}$

⇒ x = 1

∴ The value of x in the given expression = 1