1.

Simplify:`1/sqrt[11-2sqrt30]`-`3/sqrt[7-2sqrt10]`-`4/sqrt[8+4sqrt3]`

Answer» `1/sqrt(11-2sqrt30) = 1/sqrt(11-2sqrt30)xxsqrt(11+2sqrt30)/sqrt(11+2sqrt30)`
`=sqrt(11+2sqrt30)/(121-120) = sqrt(11+2sqrt30)`

`3/(sqrt(7-2sqrt10)) = 3/sqrt(7-2sqrt10)xxsqrt(7+2sqrt10)/(sqrt(7+2sqrt10)`
`=(3sqrt(7+2sqrt10))/(49-40) = sqrt(7+2sqrt10)`

`4/sqrt(8+4sqrt3) = 4/sqrt(8+4sqrt3)xxsqrt(8-4sqrt3)/sqrt(8-4sqrt3)`
`=(4sqrt(8-4sqrt3))/(64-48) = sqrt(8-4sqrt3)= sqrt(8-2sqrt12)`

`:. 1/sqrt(11-2sqrt30) - 3/(sqrt(7-2sqrt10)) - 4/sqrt(8+4sqrt3) =sqrt(11+2sqrt30) - sqrt(7+2sqrt10)-sqrt(8-2sqrt12)`
`=sqrt(sqrt6^2+sqrt5^2+2sqrt6sqrt5)-sqrt(sqrt5^2+sqrt2^2+2sqrt2sqrt5)-sqrt(sqrt6^2+sqrt2^2-2sqrt6sqrt2`
`=sqrt((sqrt6+sqrt5)^2)-sqrt((sqrt5+sqrt2)^2)-((sqrt6-sqrt2)^2)`
`=sqrt6+sqrt5-sqrt5-sqrt2-sqrt6+sqrt2 = 0`


Discussion

No Comment Found

Related InterviewSolutions