Question

solve this question please very important

Answer 1

Given a + √b = c + √d

Case (i): Let a=c ⇒ a + √b = c + √d becomes a + √b = a + √d ⇒ √b = √d ∴ b = d

Case (ii): Let a ≠ c Let us take a = c + k where k is a rational number not equal to zero.

⇒ a + √b = c + √d becomes (c + k) + √b = c + √d

⇒ k + √b = √d Let us now square on both the sides,

⇒ (k + √b)2 = (√d)2 ⇒ k2 + b + 2k√b = d

⇒ 2k√b = d – k2 – b Notice that the RHS is a rational number.