Question

COMPREHENSION TYPE:
(x-a)(x-b)=x²+x+4 Based on the above answer the following
(1) 1/a^2 + 1/b^2 =
(2) (a/b - b/a)^2 =
(3) a^2 - b^2=​

Answer 1

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

= x2 - xb + ax - ab

= x2 + (a - b)x - ab

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

= x2 + xb - ax - ab

= x2 - (a - b)x – ab

Thus, we have

(x + a)(x + b) = x2 + (b + a)x + ab

(x - a)(x - b) = x2 - (b + a)x + ab

(x + a)(x - b) = x2 + (a - b)x - ab

(x - a)(x + b) = x2 - (a - b)x – ab

(x + a)(x + b) = x2 + (Sum of constant terms)x + Product of constant terms.