Question

If 'a' and 'b' are rational numbers,find the value of a and b in each of the following equations.
$\sqrt{3} + \sqrt{2} \div \ \sqrt{3 } - \sqrt{2} = a + b = \sqrt{6}$
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Answer 1

Answer:

Solving LHS:

=> (√3 + √2)/(√3 - √2)

Multiply and divide by √3 + √2:

=> (√3+√2)/(√3-√2) x (√3+√2)/(√3+√2)

=> (√3+√2)(√3+√2) / (√3 - √2)(√3+√2)

=> (√3+√2)² / (√3² - √2²)

=> (√3² + √2² + 2√3√2) / (3 - 2)

=> (3 + 2 + 2√6) / 1

=> 5 + 2√6

Compare this with a + b√6,

a = 5 & b = 2

Answer 2

hope this will help you.....all the best..