Question

rationalise and find a and b √5-2 √5+2 =a+b√5.​

Answer 1

Step-by-step explanation:

Question:-

Rationalise the denominator and find a and b √5-2/ √5+2 = a-b√5.

To find out:-

• The value of a and b

Solution:-

Let's solve the problem

We have,

√5 - 2/√5 + 2

The denominator is √5 +2. Multiplying the numerator and denomination by √5 - 2, we get

➡ √5 - 2/√5 + 2 × √5 - 2/√5 - 2

➡ (√5 - 2)(√5 - 2) / (√5 + 2)(√5 - 2)

⬤ Applying Algebraic Identity

• (a-b)(a-b) = (a-b)² = a² + b² - 2ab to the numerator &
• (a+b)(a-b) = a² - b² to the denominator

We get,

➡ (√5 - 2) / (√5)² - (2)²

➡ (√5)² + (2)² - 2 × 2 × √5 / 5 - 4

➡ 5 + 4 - 4√5 /1

➡ 9 - 4√5 /1

➡ 9 - 4√5

∴ a - b√5 = 9 -4√5

On comparing, the value of a = 9 and b = 4.

Answer:-

Hence, the value of a = 9 and b = 4.

Used Formulae:-

• (a-b)(a-b) = (a-b)² = a² + b² - 2ab
• (a+b)(a-b) = a² - b²

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