15 points please answer
with full explanation. correct answer will surely be marked as brainliest
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Given a² - 5 a - 1 = 0
a = [ 5 +- √(25+4) ] / 2 = [5+√29] /2 or [5 - √29 ]/2
For a = [5+√29]/2
1/a = 2/[5 +√29] = 2*(5-√29)/[(5+√29)(5-√29)]
= 2(5-√29)/(-4) = (√29 - 5) / 2
So a + 1/a = √29
For a = [5-√29]/2,
1/a = 2/[5-√29] = 2 * [5+√29] / [ (5² - 29) ]
= - [5 + √29 ] /2
So a + 1/a = - √29
Hence answer is + √29 or -√29
a = [ 5 +- √(25+4) ] / 2 = [5+√29] /2 or [5 - √29 ]/2
For a = [5+√29]/2
1/a = 2/[5 +√29] = 2*(5-√29)/[(5+√29)(5-√29)]
= 2(5-√29)/(-4) = (√29 - 5) / 2
So a + 1/a = √29
For a = [5-√29]/2,
1/a = 2/[5-√29] = 2 * [5+√29] / [ (5² - 29) ]
= - [5 + √29 ] /2
So a + 1/a = - √29
Hence answer is + √29 or -√29
kvnmurty:
:-)
do not get angry... i will correct the last line.
Np
Answered by
3
Heya user,
Given, a² - 5a - 1 = 0; ---> (1)
Clearly a ≠ 0 ;
Dividing (1) by a, we get :
----> a - 5 - 1/a = 0
==> a - 1/a = 5
==> [ a - 1/a ]² = 5²
==> a² + 1/a² - 2 = 25
==> a² + 1/a² + 2 = 25 + 4
==> [ a + 1/a ]² = 29
==> a + 1/a = + √29 or - √29
Given, a² - 5a - 1 = 0; ---> (1)
Clearly a ≠ 0 ;
Dividing (1) by a, we get :
----> a - 5 - 1/a = 0
==> a - 1/a = 5
==> [ a - 1/a ]² = 5²
==> a² + 1/a² - 2 = 25
==> a² + 1/a² + 2 = 25 + 4
==> [ a + 1/a ]² = 29
==> a + 1/a = + √29 or - √29
good . one. right. your previous answer was ill formatted. and it gave wrong answer. so it was deleted.
sorry for the trouble caused.
good luck @Ansh290602
this answer is well written... also easily understood. congratulations.
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