Question

If a = 1+√2009/2
,then (a^3 – 503a + 500)^10 =

1) 3^10
2) 2^10
3) 5^10
4) 4^10​
plz answer I'll mark as brainliest

Answer 1

(a³ - 503a - 500)¹⁰ = 2¹⁰ ; a = (1 + √2009)/2

Step-by-step explanation:

Given, a = (1 + √2009)/2

∴ (a³ - 503a - 500)¹⁰

= [{(1 + √2009)/2}³ - 503 (1 + √2009)/2 - 500]¹⁰

= [(1 + √2009)/2 * {(1 + √2009)/2}² - 503 (1 + √2009)/2 - 500]¹⁰

= [(1 + √2009)/2 * {(1 + 2√2009 + 2009)/4 - 503} - 500]¹⁰

= [(1 + √2009)/2 * {(2010 + 2√2009 - 2012)/4} - 500]¹⁰

= [(1 + √2009)/2 * (- 2 + 2√2009)/4 - 500]¹⁰

= [(√2009 + 1)/2 * (√2009 - 1)/2 - 500]¹⁰

= [(2009 - 1)/4 - 500]¹⁰

= [2008/4 - 500]¹⁰

= [502 - 500]¹⁰

= 2¹⁰

Therefore option (b) = 2¹⁰ is correct.