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C3 - Algebraic fractions help please !!

Ive attatched a copy of the question I need help with part b

What I did was

x^2+x+1>0

(x+0.5)^2 -1/4+1 > 0

(x+0.5x)^2 +3/4 > 0

Is this enough to show what else should I write ?

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Reply 1

electriic_ink

Olive123

You've got the right idea but you've set your answer out wrong. You can't start your answer by writing x^2+x+1>0 because you don't know that yet! Instead, you should say something like:

x^2+x+1 = (x+0.5)^2 +3/4
And since (x+0.5)^2 is greater than or equal to zero, (x+0.5)^2 +3/4 ≥ 3/4 > 0
Therefore, x^2+x+1 > 0

(edited 11 years ago)

Reply 2

raheem94

Original post by Olive123

Ive attatched a copy of the question I need help with part b

What I did was

x^2+x+1>0

(x+0.5)^2 -1/4+1 > 0

(x+0.5x)^2 +3/4 > 0

Is this enough to show what else should I write ?

This isn't enough.

You need to say

(x+0.5)^2 \ge 0

for all values of

x

(x+0.5)^2 + \dfrac34 \ge \dfrac34

for all values of

x

(edited 11 years ago)

Reply 3

raheem94

Original post by electriic_ink

You've got the right idea but you've set your answer out wrong. You can't start your answer by writing x^2+x+1>0 because you don't know that yet! Instead, you should say something like:

x^2+x+1 = (x+0.5x)^2 +3/4
And since (x+0.5x)^2 is greater than or equal to zero, (x+0.5x)^2 +3/4 >= 3/4 > 0
Therefore, x^2+x+1 > 0