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If a is such a constant so that 9x^2 + 24x + a + 6x + x^2 is the square of a bionamal. What is a?

 Apr 6, 2022
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9x^2 + 24x + a  + 6x + x^2  =

 

10x^2 + 30x   +  a

 

We need     

 

( [sqrt 10] x   + sqrt a ) ( [sqrt 10 ] x  + sqrt a )

 

So that

 

2 sqrt (10 a)   =  30

 

sqrt (10a) = 15      square both sides

 

10a  = 225

 

a  = 225 /10  =  22.5

 

Check

 

( [sqrt (10)x + sqrt (22.5) ] ^2 =

 

10x^2 + 2 ( sqrt 10 * sqrt 22.5 )x  + 22.5  =

 

10x^2 + 2 sqrt (225) x  + 22.5  =

 

10x^2 +  2 * 15x   + 22.5   =

 

10x^2 + 30x + 22.5

 

cool cool cool

 Apr 6, 2022

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