Answer:
Firstly, we'll apply the below identity.
[tex]{\boxed{\sf{(a+b)^{2} = a^{2} + b^{2} +2ab}}}[/tex]
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.
