Find numbers a , b , p and q so that: x 3 </msup> + 1

Zion Wheeler

Zion Wheeler

Answered question

2022-06-23

Find numbers a, b, p and q so that:
x 3 + 15 x 2 + 3 x + 5 = p ( x a ) 3 + q ( x b ) 3

Answer & Explanation

Haggar72

Haggar72

Beginner2022-06-24Added 25 answers

3 p a 2 + 3 q b 2 = 3 p a 2 + q b 2 = 1
You have also p + q = 1. So p a 2 + q b 2 = p + q = 1 from here we conclude that a = ± 1 , b = ± 1.
3 p a 3 q b = 15 p a + q b = 5
Using p a + q b = 5 and p + q = 1 with a = 1 , b = 1 you find p = 2 and q = + 3
Using p a + q b = 5 and p + q = 1 with a = 1 , b = 1 you find p = 3 and q = 2. Therefore the solution is
( a , b , p , q ) = ( 1 , 1 , 2 , 3 ) & ( a , b , p , q ) = ( 1 , 1 , 3 , 2 )
Peyton Velez

Peyton Velez

Beginner2022-06-25Added 2 answers

( p , q ) and ( p a 2 , q b 2 ) both obey the same pair of linear equations.So either the pair of equations is degenerate, or the two vectors are equal.

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