Question

simply each
1.(5+✓5) (5-✓5)
2.(4+2✓5) + (2+3✓5
3.(7+✓6) raise to 2​

Answer 1

Answer:

1. 20

2. 6 + 5√5

3. 55 + 14√6

Step-by-step explanation:

1. (5 + √5)(5 - √5)

• { Identity : (a + b)(a - b) = a² - b²

Here, a = 5, b = √5 }

→ (5)² - (√5)²

→ 25 - 5

→ 20

2. (4 + 2√5) + (2 + 3√5)

→ 4 + 2√5 + 2 + 3√5

→ 4 + 2 + 2√5 + 3√5

→ 6 + 5√5

3. (7 + √6)²

• {Identity : (a + b)² = a² + 2ab + b²

Here, a = 7, b = √6 }

→ (7)² + 2(7)(√6) + (√6)²

→ 49 + 14√6 + 6

→ 55 + 14√6

Answer 2

$\Huge{\underline{\boxed{\bf{\orange{Answer\::}}}}}$

1. 20.

2. 6 + 5√5.

3. 55 + 14√6.

• Step by step explaination :-

1) (5 + √5) (5 - 5√5)

● We know equation :-

${(a + b)\:(a - b)\:= {a}^{2} - {b}^{2}}$

Here a = 5, b = √5

${5}^{2} -{\sqrt{5}^{2}}$

$\to\text{25\:-\:5}$

$\to{\text{\red{20}}}$

$\rule{300}2$

2) (4 + 2√5) + (2 + 3√5)

(4 + 2√5 + 2 + 3√5)

(4 + 2 +2√5 + 3√5)

(6 + 5√5)

$\rule{300}2$

3) (7 + √6)²

● We know equation :-

${{(a\:+\:b)}^{2}\:={\:{a}^{2}\:+\:2ab\:+{b}^{2}}}$

Here a = 7, b = √6

7² × 2(2) × √6 + (√6)²

49 + 14√6 × 6

→ 55 + 14√6