Q. 1 G4.2( 5 Votes )

Solve the followi

Answer :

Now in the above quadratic equation the coefficient of x2 is 4. Let us make it unity by dividing the entire quadratic equation by 4.

4x2 + 4bx – (a2 – b2) = 0

x2 + bx = (a2 – b2)/4

Now by taking half of the coefficient of x and then squaring it and adding on both LHS and RHS sides.

Coefficient of x = b

Half of b = b/2

Squaring the half of b = b/4

Now the LHS term is a perfect square and can be expressed in the form of (a-b) 2 = a2 – 2ab + b2 where a = x and b = b/2

On simplifying both RHS and LHS we get an equation of following form,

(x ± A)2 = k2

Taking Square root of both sides.

Now taking the positive part,

x = (a – b) / 2

Now taking the negative part,

x = - (a + b) / 2

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