Question

if root3 + root7/ root3 - root7 = a+b root7 find a and b.

Answer 1

$\underline{\underline{\boxed{\red{\sf Question}}}}$

$\sf \: \dfrac{3 + \sqrt{7} }{3 - \sqrt{7} } = a + b \sqrt{7}$

$\underline{\underline{\boxed{\blue{\sf Answer \ a= 8 b = 3}}}}$

$\underline{\underline{\boxed{\pink{\sf Step ~by ~step~ explanation }}}}$

Given

• $\sf \: \dfrac{3 + \sqrt{7} }{3 - \sqrt{7} } = a + b \sqrt{7}$

To Find

• Value of a and b.

Solution

${ \implies\sf \: \dfrac{3 + \sqrt{7} }{3 - \sqrt{7} }}$

$\text{\gray{On Rersonalising The Denominator Term}}$

${ \implies\sf \: \dfrac{3 + \sqrt{7} }{3 - \sqrt{7} }} \times \sf \: \dfrac{3 + \sqrt{7} }{3 + \sqrt{7} }$

${ \implies\sf \: \dfrac{(3 + \sqrt{7} ) ^{2} }{3 ^{2} - (\sqrt{7} )^{2} }}$

${ \implies\sf \: \dfrac{9 + 7 + 6 \sqrt{7} }{9 - {7} }}$

${ \implies\sf \: \dfrac{16 + 6 \sqrt{7} }{2 }}$

${ \implies\sf \: 8 + 3 \sqrt{7} }$

According To Question

${ \implies\sf \: 8 + 3 \sqrt{7} = a + b \sqrt{7} }$

• $\sf \: a = 8 \\ \sf \: b = 3$

Answer 2

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

Question

$\sf \: \dfrac{3 + \sqrt{7} }{3 - \sqrt{7} } = a + b \sqrt{7}$

$\underline{\underline{\boxed{\blue{\sf Answer \ a= 8 b = 3}}}}$

$\underline{\underline{\boxed{\pink{\sf Step ~by ~step~ explanation }}}}$

Given

$\sf \: \dfrac{3 + \sqrt{7} }{3 - \sqrt{7} } = a + b \sqrt{7}$

To Find

Value of a and b.

Solution

${ \implies\sf \: \dfrac{3 + \sqrt{7} }{3 - \sqrt{7} }}$

$\text{\gray{On Rersonalising The Denominator Term}}$

${ \implies\sf \: \dfrac{3 + \sqrt{7} }{3 - \sqrt{7} }} \times \sf \: \dfrac{3 + \sqrt{7} }{3 + \sqrt{7} }$

${ \implies\sf \: \dfrac{(3 + \sqrt{7} ) ^{2} }{3 ^{2} - (\sqrt{7} )^{2} }}$

${ \implies\sf \: \dfrac{9 + 7 + 6 \sqrt{7} }{9 - {7} }}$

${ \implies\sf \: \dfrac{16 + 6 \sqrt{7} }{2 }}$

${ \implies\sf \: 8 + 3 \sqrt{7} }$

According To Question

${ \implies\sf \: 8 + 3 \sqrt{7} = a + b \sqrt{7} }$

$\begin{gathered} \sf \: a = 8 \\ \sf \: b = 3\end{gathered}$