1.

A and b are rational numbers2+√3 / 3√2-2√3 = a+b√6Find a and b

Answer»

ANSWER:

The VALUES a = 7 and b = 4

Step-by-step explanation:

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

2−

3

2+

3

=a+b

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}

2−

3

2+

3

×

2+

3

2+

3

=a+b

3

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

(2−

3

)(2+

3

)

(2+

3

)

2

=a+b

3

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

(2)

2

−(

3

)

2

4+3+4

3

=a+b

3

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

4−3

7+4

3

=a+b

3

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

3

=a+b

3

Compare both the sides,

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


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