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

Last updated at Dec. 16, 2024 by

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

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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

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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 and Computer Science at Teachoo