Radicals + Sines = Headache

Geometry Level 5

4 sin ⁡ 2 7 ∘ = a + b − c − d \large 4\sin { 27^\circ } =\sqrt { a+\sqrt { b } } -\sqrt { c-\sqrt { d } }

Given that a , b , c a,b,c and d d are positive integers that satisfy the equation above with b b and d d are square free and at least 2 2 of a , b , c , d a,b,c,d are equal, find a + b + c + d a+b+c+d .


The answer is 18.

Shivamani Patil by shivamani patil , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

4 ∗ S i n 2 7 o = 4 ∗ 1 4 ∗ { 5 + 5 − 3 − 5 } = { a + b − c − d } a + b + c + d = 18 4*Sin27^o =4*\dfrac 1 4 *\left \{\sqrt{ 5 + \sqrt5 } - \sqrt{ 3 - \sqrt5 } \right \}\\ =\left \{ \sqrt { a + \sqrt b } - \sqrt {c - \sqrt d } \right \} \\a+b+c+d= ~~~~~\Large \color{#D61F06}{18}

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Vraj Mistry
Jun 30, 2015

=

0 Helpful 0 Interesting 0 Brilliant 0 Confused

at least 2 of a , b , c , d are equal !

mohamed atef - 5 years, 11 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...