If x = 1/(2 − √3), find the value of x^3 − 2x^2 − 7x + 5 - [Video] - T

If x = 1/(2 − √3), find the value of x^3 − 2x^2 − 7x + 5 - Part 2
If x = 1/(2 − √3), find the value of x^3 − 2x^2 − 7x + 5 - Part 3


Transcript

If x = 1/(2 − √3), find the value of x3 − 2x2 − 7x + 5 Let us first rationalise x x = 1/(2 − √3) = 1/(2 − √3) × (2 + √3)/(2 + √3) = (2 + √3)/(2^2 − (√3)^2 ) = (2 + √3)/(4 − 3) Now, x2 = (2 + √3)^2 = 〖2^2+(√3)〗^2 + 4√3 And, x3 = (2 + √3)^3 = 〖2^3+(√3)〗^3 + 3 × 2 × √3 (2 + √3) = 8+3√3 +6√3 (2 + √3) = 8+3√3 +12√3+18 Now, x3 − 2x2 − 7x + 5 = (26+15√3) − 2(7 +4√3) − 7(2 + √3 ) + 5 = 26+15√3 −14 −8√3−14−7√3+5 = (26+5−14−14)+(15√3 −8√3−7√3) = 𝟑

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.