Question

If 5 + 2 root 3 / 7 + 4 root 3 = a - b root 3, find a and b.​

Answer 1

Answer:

a = 11, b = 6

Step-by-step explanation:

Given

$\frac{5+2\sqrt{3} }{7+4\sqrt{3} }$

Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.

The conjugate of 7 + 4$\sqrt{3}$ is 7 - 4$\sqrt{3}$

= $\frac{(5+2\sqrt{3})(7-4\sqrt{3}) }{(7+4\sqrt{3})(7-4\sqrt{3} }$ ← expand numerator/ denominator using FOIL

= $\frac{35-20\sqrt{3}+14\sqrt{3}-24 }{49-28\sqrt{3}+28\sqrt{3}-48 }$

= $\frac{11-6\sqrt{3} }{1}$

= 11 - 6$\sqrt{3}$

with a = 11 and b = 6

Answer 2

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√3)²]

=[11-6√3]/[49-48]

=11-6√3

therefore

11-6√3 = a+b√3

compare both sides

a= 11, b= -6

Step-by-step explanation:

Hope this answer helps you :)

Have a great day

Mark brainliest