If a= 1-√3, find the value of (𝑎−1/𝑎)^3.

Asked by v.venkateshalu | 1st Feb, 2021, 10:17: AM

Expert Answer:

Given: a= 1-√3
open parentheses straight a minus 1 over straight a close parentheses cubed equals open parentheses 1 minus square root of 3 minus fraction numerator 1 over denominator 1 minus square root of 3 end fraction close parentheses cubed
equals open parentheses 1 minus square root of 3 minus fraction numerator 1 plus square root of 3 over denominator negative 2 end fraction close parentheses cubed
equals open parentheses fraction numerator 2 minus 2 square root of 3 plus 1 plus square root of 3 over denominator 2 end fraction close parentheses cubed
equals open parentheses fraction numerator 3 minus square root of 3 over denominator 2 end fraction close parentheses cubed
equals fraction numerator 27 minus 3 square root of 3 minus 27 square root of 3 plus 27 over denominator 8 end fraction
equals fraction numerator 54 minus 30 square root of 3 over denominator 8 end fraction

Answered by Renu Varma | 3rd Feb, 2021, 04:45: PM