Question

pls tell value of a and b​

Answer 1

Answer:

Given :-

$\sf \: \dfrac{5 + \sqrt{3} }{7 - 4 \sqrt{3} } = 47a + \sqrt{3b}$

To Find :-

a and b

Solution :-

At first lets simply RHS

RHS = $\sf \: \dfrac{5 + \sqrt{3} }{7 - 4 \sqrt{3} }$

5 + √3/7 - 4√3 × 7 + 4√3/ 7 - 4√3

(5 + √3) (7 + 4√3)

(5)(7) + (5)(4)√3 + (1)(7)√3 + 12

35 + 20√3 + 7√3+12

47 + 27√3 = 47a + √3b

a = 1 and b = 26

Answer 2

Solution :

$\displaystyle \bold{ \sf{ Given \: - }} \\ \\ \implies{ 47a + \sqrt{3} b = \dfrac{ 5 + \sqrt{3} }{ 7 - 4\sqrt{3} }} \\ \\ \tt{ Let \: us \: simplify \: the \: RHS \: - } \\ \\ \implies{ \dfrac{ 5 + \sqrt{3} }{ 7 - 4\sqrt{3} }} \\ \\ \implies {\bold{ Rationalising \: - }} \\ \\ \implies{ \dfrac{ 5 + \sqrt{3} }{ 7 - 4\sqrt{3} } \times \dfrac{ 7 + 4\sqrt{3} }{ 7 - 4\sqrt{3}} }$ $\implies{ ( 5 + \sqrt{3} )( 7 + 4 \sqrt{3} ) } \\ \\ \implies{ 35 + 20 \sqrt {3} + 7 \sqrt{3} + 12 } \\ \\ \implies{ 47 + 27 \sqrt{3} } \\ \\ \tt{ This \: is \: equal \: to \: 47a \: + \: \sqrt{3}b } \\ \\ \implies{ Hence \: - } \\ \\ \sf{ a = 1 \: \& \: b = 26 } \\ \\ \tt{ \orange{ This \: is \: the \: required \: answer. }}$