Question

if 7√3/√10+√3 plz ans fast with explanation ​

Answer 1

Answer:

$\implies \dfrac{a}{b} = \dfrac{ - 3}{ \sqrt{3}}$

Explanation:

Given,

$\implies \: \dfrac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } = a + b \sqrt{10}$

Taking L. H. S. :-

$= \dfrac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} }$

Rationalizing the denominator,

$= \dfrac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } \times \dfrac{ \sqrt{10} - \sqrt{3} }{ \sqrt{10} - \sqrt{3} }$

${ = \dfrac{(7 \sqrt{3})( \sqrt{10} - \sqrt{3} ) }{ {( \sqrt{10}) }^{2} - {( \sqrt{3}) }^{2} } \:\:\:\:\:\:\:\:\: \boldsymbol{[\because (a + b)(a - b) = a^2 - b^2]}}$

$= \dfrac{7 \sqrt{30} - 21}{10 - 3}$

$= \dfrac{7 \sqrt{30} - 21}{7}$

$= \dfrac{7 \sqrt{30} }{7} - \dfrac{21}{7}$

$= \sqrt{30} - 3$

On comapring with R. H. S. :- a + b√3

$\implies \: \sqrt{30} - 3 = a+ b \sqrt{10}$

$\implies \: - 3 + \sqrt{30} =a + b \sqrt{10}$

$\implies \: a = - 3 \: { \rm \: and} \: b = \sqrt{3}$

Hence,

$\implies \dfrac{a}{b} = \dfrac{ - 3}{ \sqrt{3} }$

$\orange{ \underline{ \therefore\sf \: Required \: answer : \green{ \dfrac{ - 3}{ \sqrt{3} }} }}$

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Identity used -

• (a + b)(a - b) = a² - b²