complete solution set of the equation |x^2-3|+|2-x|=|x^2-x-1|

Asked by rajshekhara348 | 20th Jun, 2022, 11:23: PM

Expert Answer:

open vertical bar straight x squared minus 3 close vertical bar plus open vertical bar 2 minus straight x close vertical bar equals open vertical bar straight x squared minus straight x minus 1 close vertical bar
rightwards double arrow open vertical bar open parentheses straight x minus square root of 3 close parentheses open parentheses straight x plus square root of 3 close parentheses close vertical bar plus open vertical bar 2 minus straight x close vertical bar equals open vertical bar open parentheses straight x minus fraction numerator 1 plus square root of 5 over denominator 2 end fraction close parentheses open parentheses straight x minus fraction numerator 1 minus square root of 5 over denominator 2 end fraction close parentheses close vertical bar
When space straight x greater than 2 greater than square root of 3
rightwards double arrow open parentheses straight x minus square root of 3 close parentheses open parentheses straight x plus square root of 3 close parentheses minus left parenthesis 2 minus straight x right parenthesis equals open parentheses straight x minus fraction numerator 1 plus square root of 5 over denominator 2 end fraction close parentheses open parentheses straight x minus fraction numerator 1 minus square root of 5 over denominator 2 end fraction close parentheses
rightwards double arrow straight x squared minus 3 minus 2 plus straight x equals straight x squared minus straight x minus 1
rightwards double arrow negative 4 equals negative 2 straight x
rightwards double arrow straight x equals 2

Similarly comma space solve space for space straight x less than 2 comma space straight x less than square root of 3 space and space straight x less than fraction numerator 1 plus square root of 5 over denominator 2 end fraction

Answered by Renu Varma | 21st Jun, 2022, 11:13: AM