Question

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

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The values of a and b​ are 11 and 6 respectively.

Step-by-step explanation:

Consider the given equation is

$\dfrac{5+2\sqrt{3}}{7+4\sqrt{3}}=a-b\sqrt{3}$

We need to find the values of a and b.

Rationalize the left hand side.

$\dfrac{5+2\sqrt{3}}{7+4\sqrt{3}}\times \dfrac{7-4\sqrt{3}}{7-4\sqrt{3}}=a-b\sqrt{3}$

$\dfrac{(5+2\sqrt{3})(7-4\sqrt{3})}{(7)^2-(4\sqrt{3})^2}=a-b\sqrt{3}$

$\dfrac{5\cdot \:7-5\cdot \:4\sqrt{3}+2\cdot \:7\sqrt{3}-2\cdot \:4\sqrt{3}\sqrt{3}}{49-48}=a-b\sqrt{3}$

$\dfrac{11-6\sqrt{3}}{1}=a-b\sqrt{3}$

$11-6\sqrt{3}=a-b\sqrt{3}$

On comparing both sides we get

$a=11,b=6$

Therefore, the values of a and b​ are 11 and 6 respectively.

#Learn more

Find the value of a and b if root 7 - root 3 / root 7 + root 3 = a - b root 21.

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