Question

√3-1/√3+1=a+b√3 then a^2+b^2=?

Answer 1

Answer:

Hi

Plz check the attached image

Answer 2

ANSWER :–

a² + b² = 5

EXPLANATION :–

GIVEN :–

• ${ \: \: \: \: \bold { \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1 } = a + b \sqrt{3} } }$

TO FIND :–

a² + b² = ?

SOLUTION :–

• According to the question –

$\\ \: \: { \implies \bold { \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1 } = a + b \sqrt{3} }}$

• Now rationalization –

$\\ \: \: { \implies \bold { \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1 } \times \frac{ \sqrt{3} - 1}{ \sqrt{3} - 1} = a + b \sqrt{3} }}$

$\\ \: \: { \implies \bold { \frac{ {( \sqrt{3} - 1) }^{2} }{ {( \sqrt{3} )}^{2} - {(1)}^{2} } = a + b \sqrt{3} }}$

$\\ \: \: { \implies \bold { \frac{3 + 1 - 2 \sqrt{3} }{3 - 1} = a + b \sqrt{3} }}$

$\\ \: \: { \implies \bold { \frac{4 - 2 \sqrt{3} }{2} = a + b \sqrt{3} }}$

$\\ \: \: { \implies \bold { 2 - \sqrt{3} = a + b \sqrt{3} }}$

• Now compare –

=> a = 2 and b = -1

• Now we have to find –

=> a² + b² = (2)² + (-1)²

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$= 4 + 1 = 5