if 3x3+ 4x2+ 7x + 9=3479, and "x" is a positive real number, what is the value of x3+ 5x2+ 7?

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Answer :

We have  : 3x3 + 4x2 + 7x  + 9 = 3479

So we can write it As  :

3x3 + 4x2 + 7x  + 9 - 3479 = 0

3x3 + 4x2 + 7x  - 3470 = 0

3x3 + 34x2 - 30x2 + 347x  - 340x  - 3470 = 0

3x3 + 34x2 + 347x - 30x2   - 340x  - 3470 = 0

x (  3x2  + 34x+ 347 ) - 10 (  3x2  + 34x+ 347 ) = 0

( x - 10 ) (  3x2  + 34x+ 347 ) = 0

So,
x  =  10 , that is a positive real number , So

And

For 3x2  + 34x+ 347  , we check

b2 -  4ac  = 342 - 4 ×× 347   = 1156 - 4164  = -3008  , So 

3x2  + 34x+ 347  Does not give any real value of x

So,
x  =  10 put in

x3 + 5x2 + 7  = 103 + 5 ( 10 )2 + 7 =  1000 + 500 + 7  =  1507  ( Ans )

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