Question

Find the values of a and b if
√2+√3/3√2-2√3
= a-b√6​

Answer 1

Answer:

please select my answer as brainilist answer please the value is 2',22

Answer 2

Step-by-step explanation:

Question:-

$\mathrm{Find \: the values \: of \: a \: and \: b \: if : }$

$\frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } = \mathrm{a - b \sqrt{6} }$

Solution:-

$\frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } = \mathrm{a - b \sqrt{6} }$

The denominator is 3√2-2√3. Multiplying the numerator and denomination by 3√2+2√3, we get

$⟹ \frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{ 3 } } \times \frac{3 \sqrt{2} + 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} }$

$⟹ \frac{( \sqrt{2} + \sqrt{3} )(3 \sqrt{2} + 2 \sqrt{3} )}{(3 \sqrt{2} - 2 \sqrt{3})(3 \sqrt{2} + 2 \sqrt{3} ) }$

1. We multiplying numerator left side to right side
2. ⬤ Applying Algebraic Identity

• (a-b)(a+b) = a² - b² to the denominator

We get,

$⟹ \frac{3 \sqrt{2 \times 2} + 2 \sqrt{3 \times 2} + 3 \sqrt{2 \times 3} + 2 \sqrt{3 \times 3} }{(3 \sqrt{2} {)}^{2} - (2 \sqrt{3} {)}^{2} }$

$⟹ \frac{3 \times 2 + 2 \sqrt{6} + 3 \sqrt{6} + 2 \times 3 }{18 - 12}$

$⟹ \frac{12 + 5 \sqrt{6} }{6}$

$⟹2 + \frac{5}{6} \sqrt{6}$

$\mathrm{∴ \: a - b \sqrt{6} = 2 + \frac{5}{6} \sqrt{6} }$

On comparing:

$\mathrm{The \: value \: of \: a = 2 \: and \: b = - \frac{5}{6} }$

Answer:-

$\mathrm{The \: value \: of \: a = 2 \: and \: b = - \frac{5}{6} }$

Used formulae:-

• (a-b)(a+b) = a² - b².

:)