Question

if a and b are rational number and 2 + √3 / 2 -√3 = a + b root √3, find the value of a and b

Answer 1

Answer:

The values a = 7 and b = 4

Step-by-step explanation:

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

we need to find the value of a and b

Rationalize the left hand side of given expression,

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

$\frac{(2+ \sqrt{3})^{2}}{(2-\sqrt{3})(2+\sqrt{3})}= a+ b \sqrt{3}$

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

$\frac{7+4\sqrt{3}}{4-3}= a+ b \sqrt{3}$

$7+4\sqrt{3}= a+ b \sqrt{3}$

Compare both the sides,

so, we get the values a = 7 and b = 4

Answer 2

Answer:

Step-by-step explanation: