if a and b are rational number find the value of a and b in √3+√2/√3-√2
Answers
Step-by-step explanation:
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 = 4
Answer:
Hope it helps!! Mark this answer as brainliest if u found it useful and follow me for quick and accurate answers...
