Disassemble rifle

Algebra Level 3

6 + 2 3 + 2 2 + 2 6 1 5 2 6 = ? \sqrt{6+2\sqrt3 + 2\sqrt2 + 2\sqrt6} - \dfrac1{\sqrt{5-2\sqrt6}} = \, ?

Give your answer to 3 decimal places.


The answer is 1.

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

Rohit Udaiwal
Dec 6, 2015

Notice that 6 + 2 6 + 2 3 + 2 2 = ( 2 + 3 + 1 ) 2 6+2\sqrt6+2\sqrt3+2\sqrt2=(\sqrt2+\sqrt3+1)^{2} and 1 5 2 6 = 1 ( 3 2 ) 2 ) . \dfrac{1}{5-2\sqrt{6}}=\dfrac{1}{(\sqrt3-\sqrt2)^{2})}.

Now our expression becomes, ( 2 + 3 + 1 ) 2 1 ( 3 2 ) 2 = 2 + 3 + 1 1 3 2 = 2 + 3 + 1 ( 3 + 2 ) 1 = 1 . \sqrt{(\sqrt2+\sqrt3+1)^{2}}-\dfrac{1}{\sqrt{(\sqrt3-\sqrt2)^{2}}} \\ =\sqrt2+\sqrt3+1-\dfrac{1}{\sqrt3-\sqrt2} \\=\sqrt2+\sqrt3+1-\dfrac{(\sqrt3+\sqrt2)}{1} \\ =\boxed{1}.

A little mistake in the first Line. Otherwise a fine solution

Shreyash Rai - 5 years, 6 months ago

Log in to reply

Thanks,made the change!

Rohit Udaiwal - 5 years, 6 months ago

Log in to reply

No problem

Shreyash Rai - 5 years, 6 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...