Question

(x+a)(x+b)=x^{​​​​​​2} + (a+b)x +ab. Evaluate 99×106 without multiplying directly.

Answer 1

102.5 -3.5 = 99
102.5 + 3.5 = 106

Therefore 99 x 106 = (102.5 -3.5) x (102.5 + 3.5) = (x+a)(x+b)
=> x = 102.5
=> a = -3.5
=> b = 3.5

x^{​​​​​​2} + (a+b)x +ab = 10506.25 + (-3.5 + 3.5)x 102.5 + (-3.5 x 3.5)
=10506.25 - 12.25
= 10494