Golden Problem

Algebra Level 3

5 + 2 3 + 5 − 2 3 = a \sqrt[3]{\sqrt 5 + 2} + \sqrt[3]{\sqrt 5 - 2} = \sqrt{a}

where a a is an integer .Find the value of a a


The answer is 5.

View wiki
Danish Ahmed by Danish Ahmed , 24, 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.

1 solution

Saurav Pal
Mar 1, 2015

5 + 2 3 + 5 − 2 3 = a ⇒ 2 5 + 3 a = a a ⇒ 20 = ( a − 3 ) 2 a ⇒ a = 5. \sqrt [ 3 ]{ \sqrt { 5 } +2 } +\sqrt [ 3 ]{ \sqrt { 5 } -2 } =\sqrt { a } \\ \Rightarrow \quad 2\sqrt { 5 } +3\sqrt { a } =a\sqrt { a } \\ \Rightarrow \quad 20\quad =\quad { (a-3) }^{ 2 }a\quad \\ \Rightarrow \quad a\quad =\quad 5.\quad \\

1 Helpful 0 Interesting 0 Brilliant 0 Confused

any whole square multiplied by an integer should be equal to 20 ......................must be the hint to solve the problem quickly

Uddipan Pal - 5 years, 8 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...