Question

if 3+√2/3-√2= a+b√2, a, b=​

Answer 1

Answer:

The values of 'a' and 'b' are 11/7 and 6/7 respectively.

$\qquad$_____________

Step-by-step explanation:

Let's rationalize the denominator of LHS :

$~$

$\purple{\tt \implies \: \dfrac{3 + \sqrt{2} }{3 - \sqrt{2} } \times \bigg \{ \dfrac{3 + \sqrt{2} }{3 + \sqrt{2} } \bigg \}}$

$\:$

$\purple{ \tt \implies \: \dfrac{ {(3 + \sqrt{2} )}^{2} }{ {(3)}^{2} { - ( \sqrt{2}) }^{2} } }$

$\:$

Using the identities (a + b)² = a² + b² + 2ab and (a + b) (a – b) for the numerator and denominator respectively :

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$\purple{ \tt \implies \: \dfrac{ {(3)}^{2} + {( \sqrt{2}) }^{2} + 2 \: (3) \: ( \sqrt{2} }{9 - 2} }$

$\:$

$\purple{ \tt \implies \: \dfrac{9 + 2 + 6 \sqrt{2} }{7} }$

$\:$

$\purple{ \tt \implies \: \dfrac{11 + 6 \sqrt{2} }{7} }$

$\:$

On comparing this to RHS, we get the values as :

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$\bigstar \: \: \purple{ \: \: {\boxed{ \tt a = \dfrac{11}{7} \: \: and \: \: b = \dfrac{6}{7} }} } \: \: \bigstar$

Answer 2

Answer:

b=

$\sqrt{10}$

because 2x5=10 please mark me brain list