InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If \(\frac{{4\sqrt 3 + 5\sqrt 2 }}{{\sqrt {48} + \sqrt {18} }} = a + b\sqrt 6\), then the values of a and b respectively1). \(\frac{9}{{15}}, - \frac{4}{{15}}\)2). \(\frac{3}{{11}},\frac{4}{{33}}\)3). \(\frac{9}{{10}},\frac{2}{5}\)4). \(\frac{3}{5},\frac{4}{{15}}\) |
|
Answer» $(\BEGIN{ARRAY}{l} \frac{{4\sqrt 3 + 5\sqrt 2 }}{{\sqrt {48} + \sqrt {18} }} = a + B\sqrt 6 \\ \RIGHTARROW \frac{{4\sqrt 3 + 5\sqrt 2 }}{{\sqrt {16 \times 3} + \sqrt {9 \times 2} }} = a + b\sqrt 6 \\ \Rightarrow \frac{{4\sqrt 3 + 5\sqrt 2 }}{{4\sqrt 3 + 3\sqrt 2 }} = a + b\sqrt 6 \\ \Rightarrow \frac{{4\sqrt 3 + 3\sqrt 2 + 2\sqrt 2 }}{{4\sqrt 3 + 3\sqrt 2 }} = a + b\sqrt 6 \\ \Rightarrow 1 + \frac{{2\sqrt 2 }}{{4\sqrt 3 + 3\sqrt 2 }} = a + b\sqrt 6 \end{array})$ Multiplying and dividing $(\frac{{2\sqrt 2 }}{{4\sqrt 3 + 3\sqrt 2 }})$ by $(4\sqrt 3 - 3\sqrt 2)$ $(\Rightarrow 1 + \frac{{2\sqrt 2 }}{{4\sqrt 3 + 3\sqrt 2 }} \times \frac{{4\sqrt 3 - 3\sqrt 2 }}{{4\sqrt 3 - 3\sqrt 2 }} = a + b\sqrt 6)$ $(\begin{array}{l} \Rightarrow 1 + \frac{{8\sqrt 6 - 6 \times 2}}{{48 - 18}} = a + b\sqrt 6 \\ \Rightarrow 1 + \frac{{8\sqrt 6 - 12}}{{30}} = a + b\sqrt 6 \\ \Rightarrow 1 + \frac{{4\sqrt 6 }}{{15}} - \frac{2}{5} = a + b\sqrt 6 \\ \Rightarrow \frac{3}{5} + \frac{{4\sqrt 6 }}{{15}} = a + b\sqrt 6 \end{array})$ Comparing both sides we have, a = 3/5 and b = 4/15 |
|