If x = 1/ root5 - 2, find x3 - 2x2 - 9x + 18

Asked by nisha_vini29 | 24th May, 2017, 01:20: PM

Expert Answer:

begin mathsize 16px style straight x equals fraction numerator 1 over denominator square root of 5 begin display style minus end style begin display style 2 end style end fraction
rightwards double arrow straight x equals fraction numerator begin display style 1 end style over denominator begin display style square root of 5 minus 2 end style end fraction cross times fraction numerator square root of 5 plus 2 over denominator square root of 5 plus 2 end fraction equals fraction numerator square root of 5 plus 2 over denominator 5 minus 4 end fraction equals square root of 5 plus 2
Now comma
straight x cubed minus 2 straight x squared minus 9 straight x plus 18
equals straight x squared left parenthesis straight x minus 2 right parenthesis minus 9 left parenthesis straight x minus 2 right parenthesis
equals left parenthesis straight x minus 2 right parenthesis left parenthesis straight x squared minus 9 right parenthesis
equals open parentheses square root of 5 plus 2 minus 2 close parentheses open square brackets open parentheses square root of 5 plus 2 close parentheses squared minus 9 close square brackets
equals open parentheses square root of 5 close parentheses open square brackets 5 plus 4 square root of 5 plus 4 minus 9 close square brackets
equals square root of 5 cross times 4 square root of 5
equals 20 end style

Answered by Rashmi Khot | 24th May, 2017, 04:38: PM