Question

If both a and b are rational numbers, find the values of a and b in 5−√3 upon 2+√3 = a + b√3​

Answer 1

Answer:

a = 13 and b = -7$\sqrt{3}$.

Step-by-step explanation:

$\frac{5-\sqrt{3}}{2+\sqrt{3}} = a +b\sqrt{3}$

Now, we can rationalise the denominator so that the denominator becomes an integer.

$\frac{5-\sqrt{3}}{2+\sqrt{3}} \frac{(2-\sqrt{3}) }{(2-\sqrt{3}) }$

= $\frac{10 - 5\sqrt{3} -2\sqrt{3} + 3 }{2^{2} - \sqrt{3}^2 }$

= $\frac{13-7\sqrt{3} }{1}$

Now, 13 - 7$\sqrt{3}$  = a + b$\sqrt{3}$

This means that a = 13 and b = -7$\sqrt{3}$.

Remember to use the correct sign for b.

Answer 2

Step-by-step explanation:

Solution has been given as enclosure.