Question

which of the following fractios is the greatest​

Answer 1

This problem can be solved in 2 ways.

1st :-

a=3–√+2–√3–√−2–√

=(3–√+2–√)(3–√+2–√)(3–√−2–√)(3–√+2–√)

=(3–√+2–√)23−2

=((3–√)2+(2–√)2+2(3–√)(2–√)

=3+2+26–√

=5+26–√

b=3–√−2–√3–√+2–√

=(3–√−2–√)(3–√−2–√)(3–√+2–√)(3–√−2–√)

=(3–√−2–√)23−2

=((3–√)2+(2–√)2+−2(3–√)(2–√)

=3+2−26–√

=5−26–√

Now

a2+b2

We know that

(x+y)2=x2+y2+2xy

⟹x2+y2=(x+y)2−2xy

If we take x=a and y=b then

a2+b2

=(a+b)2−2ab

=(5+26–√+5−26–√)2−2((5+26–√)(5−26–√))

=(10)2−2(25−24)

Here we use identity