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Find the value of a in the following:
6/(3√2 - 2√3) = 3√2 - a√3

Solution:

Given, 6/(3√2 - 2√3) = 3√2 - a√3

We have to find the value of a.

By taking conjugate,

6/(3√2 - 2√3) = 6/(3√2 - 2√3) × (3√2 + 2√3)/(3√2 + 2√3)

= 6(3√2 + 2√3) / (3√2 - 2√3)(3√2 + 2√3)

a² - b² = (a + b)(a - b)

So, (3√2 - 2√3)(3√2 + 2√3) = (3√2)² - (2√3)²

= 9(2) - 4(3)

= 18 - 12

= 6

Now, 6(3√2 + 2√3) / (3√2 - 2√3)(3√2 + 2√3) = 6(3√2 + 2√3) / 6

= 3√2 + 2√3

Given, 6/(3√2 - 2√3) = 3√2 - a√3

So, 3√2 + 2√3 = 3√2 - a√3

Solving for a,

3√2 + 2√3 - 3√2 = - a√3

2√3 = -a√3

Canceling common term,

2 = -a

Therefore, a = -2

✦ Try This: Find the value of a in the following :

5/(2√2 - 3√3) = 4√2 - a√3

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1

NCERT Exemplar Class 9 Maths Exercise 1.3 Sample Problem 4

Summary:

Conjugate in math means to write the negative of the second term. The value of a in the expression 6/(3√2 - 2√3) = 3√2 - a√3 is -2

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