Question

How do you evaluate `[\frac { 3} { 2} - ( \frac { 1} { 2} - \frac { 3} { 4} ) ^ { 2} ] ^ { - 1} + [ ( 3+ \frac { 1} { 3} ) ^ { 2} - ( 3- \frac { 1} { 3} ) ^ { 2} ] ^ { - \frac { 1} { 2} }`?

Answer 1

`[3/2-((2-3)/4)^2]^-1+[((9+1)/3)^2-((9-1)/3)^2]^(-1/2)`

Explanation:

`=[3/2-((-1)/4)^2]^-1+[((10)/3)^2-((8)/3)^2]^(-1/2)=`
`=[3/2-1/8]^-1+[100/9-64/9]^(-1/2)=`
`=[(12-1)/8]^-1+[(100-64)/9]^(-1/2)=`
`=[11/8]^-1+[36/9]^(-1/2)=`
`=1/[8/11]+1/[36/9]^(1/2)=`
`=11/8+[9/36]^(1/2)=`
`=11/8+[3^2/6^2]^(1/2)=`
`=11/8+3/6=11/8+1/2=(11+4)/8=15/8`