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`        If the sum and product of sursa a+√b and c+√d both are rational, then one of the conditions to be satisfied is  1. a=b .  2. √b + √d =0  3.  a = d .  4.  b = c `
one year ago

```							Given a + √b = c + √dCase (i): Let a=c⇒ a + √b = c + √d becomesa + √b = a + √d⇒ √b = √d∴ b = dCase (ii): Let a ≠ cLet 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 = √dLet 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.Hence √b is a rational numberThis is possible only when b is square of a rational number.Thus d is also square of a rational number as k + √b = √d.... Hope it helps
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one year ago
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