Question

22. The value of (√5 + √2)^2 + (√5 – √2)^2 is equal to (a) 7 (b) 14 (c) 6 (d) 2√10​

Answer 1

Answer:

(b) 14

Step-by-step explanation:

ATQ,

${( \sqrt{5} + \sqrt{2} )}^{2} + {( \sqrt{5} - \sqrt{2} )}^{2}$

We use both of the following algebraic identities

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \\ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}$

Where

$x = \sqrt{5} \\ y = \sqrt{2}$

We get

$( {( \sqrt{5} )}^{2} + 2 \sqrt{5} \sqrt{2} + {( \sqrt{2} )}^{2} ) + ( {( \sqrt{5} )}^{2} - 2 \sqrt{5} \sqrt{2} + {( \sqrt{2} )}^{2} ) \\ (5 + 2 \sqrt{10} + 2) + (5 - 2 \sqrt{10} + 2) \\ (5 + 2) + (5 + 2) \\ 7 + 7 \\ 14$

Hence (b) is the correct option