Question

simplify

( 1 ) ( 5 + √5) ( 5 - √ 5)
( 2 ) ( 3 + 2√2 ) ( 3- 2√2)



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Answer 1

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1. $(5 + \sqrt{5} )(5 - \sqrt{5}) \\ 5 {}^{2} - 5 \sqrt{5} + 5 \sqrt{5} - \sqrt{25} \\ 25 - 5 \\ 20 \: ans \:$
2. $(3 + 2 \sqrt{2} )(3 - 2 \sqrt{2} ) \\ 3 {}^{2} - 6 \sqrt{2} + 6 \sqrt{2} - 8 \\ 9 - 8 \\ = 1ans$

Answer 2

Given :-

It is given to simplify the given expressions;

• (5 + √5)(5 - √5)
• (3 + 2√2)(3 - 2√2)

Solution :-

Here's the solutions ;

Equation 1 —

• Simplifying the first equation which is;

(5 + √5)(5 - √5)

⇒ 5² - (√5)²

⇒ 25 - (√5)²

⇒ 25 - 5

⇒ 20

∴ Hence, simplification of first equation will be 20.

Equation 2 —

• Simplifying the second equation which is;

(3 + 2√2)(3 - 2√2)

⇒ (3 + 2√2)²

⇒ 9 + 12√2 + 4(√2)²

⇒ 9 + 12√2 + 4 × 2

⇒ 9 + 12√2 + 8

⇒ 17 + 12√2

∴ Hence, the simplification for second equation will be 17 + 12√2.