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Hi ,
a , a² + 2 and a³ + 10 are in G. P
**************************
we know that ,
If a , b , c are in G.P then b² = ac
**************************
( a² + 2 )² = a ( a³ + 10 )
a⁴ + 4a² + 4 = a⁴ + 10a
4a² - 10a + 4 = 0
divide each term with 2 , we get
2a² - 5a + 2 = 0
2a² - 4a - a + 2 = 0
2a ( a - 2 ) - ( a - 2 ) = 0
( a - 2 ) ( 2a - 1 ) = 0
Therefore ,
a - 2 = 0 or 2a - 1 = 0
a = 2 or a = 1/2
I hope this helps you.
:)
a , a² + 2 and a³ + 10 are in G. P
**************************
we know that ,
If a , b , c are in G.P then b² = ac
**************************
( a² + 2 )² = a ( a³ + 10 )
a⁴ + 4a² + 4 = a⁴ + 10a
4a² - 10a + 4 = 0
divide each term with 2 , we get
2a² - 5a + 2 = 0
2a² - 4a - a + 2 = 0
2a ( a - 2 ) - ( a - 2 ) = 0
( a - 2 ) ( 2a - 1 ) = 0
Therefore ,
a - 2 = 0 or 2a - 1 = 0
a = 2 or a = 1/2
I hope this helps you.
:)
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