Question

How to solve square root(6)+ square root(2) = square root(5)+ square root(3)?

Answer 1

Let

√(5+2√6=√x+√y

√(5+2√6=√x+√y

5+2√6=x+y+2√xy

5+2√6=x+y+2√xy

x+y=5x+y

=5,xy=6xy=6

From here get the value of x-y which will be 1.

You can do that by gettimg x2+y2=13x2+y2=13

(x−y)2=1(x−y)2=1 From there it follows that

x−y=1x−y=1

now solve a simultaneous to get x= 3, y = 2

therefore Answer is

√3+√2