Question

Find the values of ‘β’ and ‘α’ in each of the following :

(i) (√3 +4√2)/(3√2 + 5√3) = α + β√3​

Answer 1

Answer:

considering RHS is a + b√6

a= -9/57

b = 17/57

Step-by-step explanation:

(√3+4√2)/(3√2+5√3)

= (√3+4√2)*(3√2-5√3)/(18-75)

=(3√6+24-15-20√6)/(-57)

=(17/57)√6 - 9/57

= b√6 + a

therefore, a = -9/57

b = 17/57

Answer 2

$\mathfrak \red{Given:-}$

$\tt{ \: \: \: \: \: \: \frac{ \sqrt{3} + 4 \sqrt{2} }{3 \sqrt{2} + 5 \sqrt{3} } = \alpha + \beta \sqrt{3} .}$