Question

find the values of the rational numbers A and B if 5 + 2 root 3 / 7 + 4 root 3 is equal to a + b root 3​

Answer 1

Answer:

Top answer ·

lhs = (5+2√3)/(7+4√3)= [(5+2√3)(7-4√3)]/[(7-4√3)(7+4√3)]=[35-20√3+14√3-24]/[7²-(4 ...

Step-by-step explanation:

Top answer ·

lhs = (5+2√3)/(7+4√3)= [(5+2√3)(7-4√3)]/[(7-4√3)(7+4√3)]=[35-20√3+14√3-24]/[7²-(4 ...

Answer 2

AnsWer :

a = 13 and b = 34√3.

To Find :

The value of a and b

Solution :

$\tt \dagger \: \: \: \: \: \dfrac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = a + b \sqrt{3}$

$\tt : \implies\dfrac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} }$

$\tt : \implies\dfrac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \dfrac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} }$

$\tt : \implies\dfrac{(5 + 2 \sqrt{3})(7 - 4 \sqrt{3} )}{ {7}^{2} - {(4 \sqrt{3} )}^{2} }$

$\tt : \implies\dfrac{35 - 20 \sqrt{3} - 14 \sqrt{3} - 48}{49 - 48}$

$\tt : \implies\dfrac{ - 13 - 34 \sqrt{3} }{1}$

$\tt : \implies - 13 - 34 \sqrt{3} .$

★ Taking Negative sign common.

$\tt : \implies 13 + 34 \sqrt{3}$

Where as,

$\tt : \implies a = 13. \: \: \: and \: b = 34 \sqrt{3}$

Therefore, the Value of a is 13 and b = 34√3.