Question

if root x + root Y is equal to square root of 18 + 6 into root 5 find the value of x

Answer 1

Solution:-
  _______
√18-6√5    = √a - √b
Squaring both sides.
   ______
(√18-6√5)² = (√a - √b)²
⇒ 18-6√5 = a + b - 2√a√b
⇒ 18 - 2 × (3√5) = (a + b)  - 2(√ab)
⇒ 18 - 2 × (√9×5) = (a+b) - 2(√ab)
⇒ 18 - 2 × (√45) = (a+b) - 2(√ab)
⇒ (15+3) - 2 × (√15×3) = (a+b) - 2(√ab)
Comparing on both sides,
⇒ (a+b) = 15+3
⇒ a+b = 18
Hence proved.



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