Question

IF a=√3+√2/√3-√2 and b=√3-√2/√3+√2 , FIND (a+b)²​.
plz answer this question if u know

Answer 1

If a= (√3+√2) / (√3-√2) and b= (√3-√2) / (√3+√2), then how do I find a^2+b^2?

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 (a+b)(a−b)=a2−b2

=100−2

=98

please mark brainliest

Answer 2

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