Question

if a= √3+√2/√3-√2 and b=√3-√2/√3+√2 then find value of a2 +b2

Answer 1

✳Hey dear user !!

✨Here is ur answer --

Given,,

a = √3+√2/√3-√2

On rationalizing ,,

= √3+√2 / √3-√2 * √3+√2 / √3+√2

= (√3+√2)^2 / (√3)^2-(√2)^2

= (√3)^2+(√2)^2+2*√3*√2/3-2

= 3+2+2√6 / 1

= 5+2√6

b = √3-√2 / √3+√2

On rationalizing,,

= √3-√2 / √3+√2 * √3-√2 / √3-√2

= (√3-√2)^2 / (√3)^2-(√2)^2

= (√3)^2+(√2)^2-2*√3*√2 / 3-1

= 3+2-2√6 / 1

= 5-2√6

Now, a^2 + b^2

= (5+2√6)^2 + (5-2√6)^2

=(5)^2+(2√6)^2+2*5*2√6+(5)^2+(2√6)^2-2*5*2√6

= 25+24+20√6+25+24-20√6

= 50+48

= 98....

So, a^2 + b^2 = 98.

Hope it helps u.....☺✌