If x = 1/(2 − √3), find the value of x^3 − 2x^2 − 7x + 5
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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
Rationalising
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Multiple Choice Questions - Chapter 1 Class 9 Maths
Example 16
If a and b are rational numbers and (√11 − √7)/(√11 + √7) = a – b√77, find the value of a and b
Example 17
Find the values of a and b if (7 + 3√5)/(3 + √5) – (7 − 3√5)/(3 − √5) = a+√5 b
Ex 1.4, 5 (i)
If x = 1/(2 − √3), find the value of x^3 − 2x^2 − 7x + 5 You are here
If a = 5 + 2√6 and b = 1/a, then what will be the value of a^2+b^2 ?
Example 18
Example 19 Important
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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