if X+1/X=√3 prove that x^3+1/x^3= 0

Asked by taritdasgupta1972 | 1st Jun, 2020, 10:16: PM

Expert Answer:

Given: x+1/x = root 3
To prove: x3 + 1/x3 = 0
straight x plus 1 over straight x equals square root of 3 space... space left parenthesis straight i right parenthesis
rightwards double arrow open parentheses straight x plus 1 over straight x close parentheses squared equals 3
rightwards double arrow straight x squared plus 1 over straight x squared plus 2 equals 3
rightwards double arrow straight x squared plus 1 over straight x squared equals 1 space... space left parenthesis ii right parenthesis
straight x cubed plus 1 over straight x cubed
equals open parentheses straight x plus 1 over straight x close parentheses open parentheses straight x squared plus 1 over straight x squared minus 1 close parentheses
equals square root of 3 open parentheses 1 minus 1 close parentheses space space space space... space From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
equals square root of 3 open parentheses 0 close parentheses
equals 0
Hence comma space straight x cubed plus 1 over straight x cubed equals 0

Answered by Renu Varma | 2nd Jun, 2020, 11:31: AM