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AURORKA [14]
1 year ago
5

If √5+√2=a+b√10 find a and b​

Mathematics
1 answer:
Liono4ka [1.6K]1 year ago
4 0

Answer:

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.

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