Question

please answer by explaining this ​

Answer 1

Given expression:-

• $\large{\sf{(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})}}$

Answer:

We are given expression is $\large{\sf{(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})}}$

Notice, given expression is in form of (a-b)(a+b).

We know that :

• $\large{\sf{(a-b)(a+b)\:=\: a² - b²}}$

Where,

• a = √5
• b = √2

Let expand :-

$\large{\sf{(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})}}$

$\implies\large{\sf{(\sqrt{5})²-(\sqrt{2})²}}$

$\implies\large{\sf{(5 - 2)}}$

$\implies\large{\sf{3}}$

Therefore,

• $\large{\sf{(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})\:=\:3}}$

More algebraic identities :-

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

• a² - b² = (a + b)(a - b)

• (a + b + c)² = a² + b² + c² + 2( ab + bc + ca)

• (a + b)³ = a³ + b³ + 3ab (a + b)

• (a - b)³ = a³ - b³ - 3ab (a - b)

• a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

• (a + b - c)² = a² + b² + c² + 2ab - 2bc -2ca

• a³ + b³ = (a+b)³ - 3ab (a + b)

Answer 2

Answer:

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