+0  
 
+1
54
1
avatar+544 

thank you in advance

 

 

winkwinkwink

lynx7  Apr 19, 2018

Best Answer 

 #1
avatar+646 
+3

Alright, here we go:

 

To prove that an expression is never positive, we just need to prove that the maximun value of the expression is smaller than zero.

 

We can just expand the expression. 

 

\(3(x+1)(x+7)=3x^2+24x+21\)

 

\((2x+5)^2=4x^2+20x+25\)

 

\(3x^2+24x+21- (4x^2+20x+25) = -x^2+4x-4\)

 

Factoring out the negative one, we have:


\( -(x^2-4x+4)\)

 

Since

 

\((x^2-4x+4)\)

 

is a perfect square, we can rewrite the expression like this:

 

\(-(x-2)^2\)

 

Since a square is always positive, and a negative of a square is negative, we proved that the original expression is negative, and always will be negative. 

 

I hope this answers your question and you have a wonderful day!

GYanggg  Apr 19, 2018
edited by GYanggg  Apr 19, 2018
Sort: 

1+0 Answers

 #1
avatar+646 
+3
Best Answer

Alright, here we go:

 

To prove that an expression is never positive, we just need to prove that the maximun value of the expression is smaller than zero.

 

We can just expand the expression. 

 

\(3(x+1)(x+7)=3x^2+24x+21\)

 

\((2x+5)^2=4x^2+20x+25\)

 

\(3x^2+24x+21- (4x^2+20x+25) = -x^2+4x-4\)

 

Factoring out the negative one, we have:


\( -(x^2-4x+4)\)

 

Since

 

\((x^2-4x+4)\)

 

is a perfect square, we can rewrite the expression like this:

 

\(-(x-2)^2\)

 

Since a square is always positive, and a negative of a square is negative, we proved that the original expression is negative, and always will be negative. 

 

I hope this answers your question and you have a wonderful day!

GYanggg  Apr 19, 2018
edited by GYanggg  Apr 19, 2018

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