Question

if a and b are the rational numbers and
$3 + \sqrt{8} \div 3 - \sqrt{8 } = a + b \sqrt{8}$

Answer 1

Answer:

a = 17 and b = 6

Step-by-step explanation:

According to the question,

$\dfrac{ 3 + \sqrt{8} }{3 - \sqrt{8} } = a + b\sqrt{8}\\\\\text{Rationalising the denominator we get,}\\\\\implies \dfrac{ 3 + \sqrt{8} }{ 3 - \sqrt{8} } \times \dfrac{ 3 + \sqrt{8} }{ 3 + \sqrt{8} }\\\\\\\implies \dfrac{ ( 3 + \sqrt{8} )^{2} }{ 3^2 - \sqrt{8}^{2}}\\\\\\\implies \dfrac{ 3^2 + 2(3)(\sqrt{8} ) + \sqrt{8}^2}{1}\\\\\\\implies 9 + 6\sqrt{8} + 8 = a + b\sqrt{8}\\\\\implies 17 + 6\sqrt{8} = a + b\sqrt{8}$

Comparing both sides we get,

⇒ a = 17 and b = 6

Hope it helped !!