Question

if x=1/2-√3 then find the value of x³-2x²-7x+5

Answer 1

x^3–2x^2–7x+5 when x=1/2+Г3. (Г stands for square root)

=(1/2+Г3)^3–2(1/2+Г3)^2–7(1/2+Г3)+5

=1–2(2+Г3)-7(2+Г3)^2+5(2+Г3)^3 /(2+Г3)^3

(taking Lcm….here highest power of (2+Г3)

=1-4-2Г3–7(7+4Г3)+5(26+15Г3) /(26+15Г3)

= 78+45Г3 / 26+15Г3

=3(26+15Г3) / (26+15 Г3)

=3