1
Question
a= √2-√3/√2+√3 find value of a+1/a
Open in App
Solution
a+1/a = (√2-√3)/(√2+√3 )+(√2+√3)/(√2-√3)
Cross multiply eachother and simplify
=[(√2-√3)(√2-√3)+(√2+√3)(√2+√3)]\(√2+√3) (√2-√3)
=[(√2)^2+(√3)^2-(2√2√3)+(√2)^2+(√3)^2+(2√2√3)]/[(√2)^2-(√3)^2]
=(2+3-2√6+2+3+2√6)/(2-3)
=(5+5)/(-1)
=-10
Cross multiply eachother and simplify
=[(√2-√3)(√2-√3)+(√2+√3)(√2+√3)]\(√2+√3) (√2-√3)
=[(√2)^2+(√3)^2-(2√2√3)+(√2)^2+(√3)^2+(2√2√3)]/[(√2)^2-(√3)^2]
=(2+3-2√6+2+3+2√6)/(2-3)
=(5+5)/(-1)
=-10
Suggest Corrections
0
Similar questions