Question

If √5+√2=a+b√10 find a and b​

Answer 1

Firstly, we'll apply the below identity.

`{\boxed{\sf{(a+b)^(2) = a^(2) + b^(2) +2ab}}}`

Applying the above identity.

⇒ (√5 + √2)²

⇒ (√5)² + (√2)² + 2×(√5)×(√2)

⇒ 5 + 2 + 2√10

⇒ 7 + 2√10

Comparing the LHS and RHS

⇒ 7 + 2√10 = a + b√10

∴ a = 7 and b = 2.