11. Find the value of a and b, if
3+√2
3-√2
a+b root2
Answers
Solving LHS:
Divide and multiply by
Matching the values
Then =b√2 → (6/7) = b
→ 11/7 =a
Answer:
Solving LHS:
\small{= > \frac{3+\sqrt2}{3-\sqrt2}}=>
3−
2
3+
2
Divide and multiply by \small{\frac{3+\sqrt2}{3+\sqrt2}}
3+
2
3+
2
\begin{gathered}\small{= > \frac{3+\sqrt2}{3-\sqrt2}\times \frac{3+\sqrt2}{3+\sqrt2} }\\\\\small{= > \frac{(3+\sqrt2)^2}{(3+\sqrt2)(3-\sqrt2)} } \\\\\small{= > \frac{3^2+(\sqrt2)^2+2(3)(\sqrt2)}{3^2 - (\sqrt2)^2} }\\\\\small{= > \frac{9+2+6\sqrt2}{9-2}}\\\\\small{= > \frac{11+6\sqrt2}{7}} \end{gathered}
=>
3−
2
3+
2
×
3+
2
3+
2
=>
(3+
2
)(3−
2
)
(3+
2
)
2
=>
3
2
−(
2
)
2
3
2
+(
2
)
2
+2(3)(
2
)
=>
9−2
9+2+6
2
=>
7
11+6
2
= > \frac{11}{7}+\small{\frac{6\sqrt2}{7}}=>
7
11
+
7
6
2
Matching the values
Then \frac{6\sqrt2}{7}
7
6
2
=b√2 → (6/7) = b
→ 11/7 =a