2 \(\sqrt{10}\) - 5\(\sqrt{3}\)
2 \(\sqrt{5}\) - 5\(\sqrt{6}\)
5 \(\sqrt{10}\) - 2\(\sqrt{3}\)
3 \(\sqrt{5}\) - 8\(\sqrt{6}\)
Correct answer is B
\(\sqrt{170 - 20 \sqrt{30}} = \sqrt{a} - \sqrt{b}\)
Squaring both sides,
\(170 - 20\sqrt{30} = a + b - 2\sqrt{ab}\)
Equating the rational and irrational parts, we have
\(a + b = 170 ... (1)\)
\(2 \sqrt{ab} = 20 \sqrt{30}\)
\(2 \sqrt{ab} = 2 \sqrt{30 \times 100} = 2 \sqrt{3000} \)
\(ab = 3000 ... (2)\)
From (2), \(b = \frac{3000}{a}\)
\(a + \frac{3000}{a} = 170 \implies a^{2} + 3000 = 170a\)
\(a^{2} - 170a + 3000 = 0\)
\(a^{2} - 20a - 150a + 3000 = 0\)
\(a(a - 20) - 150(a - 20) = 0\)
\(\text{a = 20 or a = 150}\)
\(\therefore b = \frac{3000}{20} = 150 ; b = \frac{3000}{150} = 20\)
\(\sqrt{170 - 20\sqrt{30}} = \sqrt{20} - \sqrt{150}\) or \(\sqrt{150} - \sqrt{20}\)
= \(2\sqrt{5} - 5\sqrt{6}\) or \(5\sqrt{6} - 2\sqrt{5}\)
A regular polygon of (2k + 1) sides has 140° as the size of each interior angle. Find k...
Find the gradient of the line joining the points (3, 2) and (1, 4) ...
The angle of elevation of the top T of a pole from a point X on the horizontal ground is 32°, if...
If Un = n(n2 + 1), evaluate U5 - U4...
\(\begin{array}{c|c} Scores & 0 - 4 & 5 - 9 & 10 - 14\\ \hline Frequency & 2 &...