Question

solve by factorisation 4x^2 - 49x + (a^2-b^2) = 0

Answer 1

49x has no solutions. However, 4ax has 2 distinct solutions...

Step-by-step explanation:

Given quadratic expression

4x²-4ax+(a²-b²)=0

=> 4x²-4ax+(a+b)(a-b)=0

/* By algebraic identity:

m²-n² =(m+n)(m-n) */

Splitting the middle term, we get

=> 4x² -2(a+b)x-2(a-b)x +(a+b)(a-b)=0

=> 2x[2x-(a+b)]-(a-b)[2x-(a+b)]=0

=> [2x-(a+b)][2x-(a-b)]=0

=> 2x-(a+b)=0 Or 2x-(a-b)=0

=> 2x = a+b Or 2x = a-b

Therefore,.

x=(a+b)/2 or (a-b)/2