What is the Conjugate of 1/4(sqrt3)-7

[hemmed]

Hi there,

I'm having real difficulty solving this, hopefully you can help. The problem is to find the conjugate of


\(\displaystyle \large{\frac{1}{4\left(\sqrt{3}-7\right)}}\)

Here are my workings out...

\(\displaystyle \large{\frac{1}{4\left(\sqrt{3}-7\right)}\:\cdot \frac{\:4\left(\sqrt{3}+7\right)}{4\left(\sqrt{3}+7\right)}\:=\:\frac{4\left(\sqrt{3}+7\right)}{-1}\:=\:-4\left(\sqrt{3}+7\right)}\)

So I get the conjugate as

\(\displaystyle \large{-4\left(\sqrt{3}-7\right)}\)

but the answer given is \(\displaystyle \large{-4\left(\sqrt{3}+7\right)}\)

I can't work out what I'm doing wrong though?

 

[Harry_the_cat]

Hi there,

I'm having real difficulty solving this, hopefully you can help. The problem is to find the conjugate of


\(\displaystyle \large{\frac{1}{4\left(\sqrt{3}-7\right)}}\)

Here are my workings out...

\(\displaystyle \large{\frac{1}{4\left(\sqrt{3}-7\right)}\:\cdot \frac{\:4\left(\sqrt{3}+7\right)}{4\left(\sqrt{3}+7\right)}\:=\:\frac{4\left(\sqrt{3}+7\right)}{-1}\:=\:-4\left(\sqrt{3}+7\right)}\)

So I get the conjugate as

\(\displaystyle \large{-4\left(\sqrt{3}-7\right)}\)

but the answer given is \(\displaystyle \large{-4\left(\sqrt{3}+7\right)}\)

I can't work out what I'm doing wrong though?

Can you confirm whether the original expression is \(\displaystyle \frac{1}{4\sqrt{3} -7}\) or \(\displaystyle \frac{1}{4(\sqrt{3}-7)}\) ?

 

[hemmed]

Can you confirm whether the original expression is \(\displaystyle \frac{1}{4\sqrt{3} -7}\) or \(\displaystyle \frac{1}{4(\sqrt{3}-7)}\) ?

Sorry, some brackets crept in! The original expression is \(\displaystyle \frac{1}{4\sqrt{3} -7}\)

 

[Harry_the_cat]

Sorry, some brackets crept in! The original expression is \(\displaystyle \frac{1}{4\sqrt{3} -7}\)

The expression is equal to \(\displaystyle -4\sqrt{3} - 7\) so the conjugate is \(\displaystyle -4\sqrt{3} + 7\).

 

[Deleted member 4993]

Hi there,

I'm having real difficulty solving this, hopefully you can help. The problem is to find the conjugate of


\(\displaystyle \large{\frac{1}{4\left(\sqrt{3}-7\right)}}\)

Here are my workings out...

\(\displaystyle \large{\frac{1}{4\left(\sqrt{3}-7\right)}\:\cdot \frac{\:4\left(\sqrt{3}+7\right)}{4\left(\sqrt{3}+7\right)}\:=\:\frac{4\left(\sqrt{3}+7\right)}{-1}\:}=\)\(\displaystyle \large{\:-4\left(\sqrt{3}+7\right)}\) ..... (1)

So I get the conjugate as (No you don't)

\(\displaystyle \large{-4\left(\sqrt{3}-7\right)}\)

but the answer given is \(\displaystyle \large{-4\left(\sqrt{3}+7\right)}\).... same as in (1)

I can't work out what I'm doing wrong though?

.

 

[hemmed]

.

Here's the content given alongside the answer...



But this doesn't make sense to me - How do you go from +7 to -7 back to +?

 

[Harry_the_cat]

Here's the content given alongside the answer...

View attachment 7681

But this doesn't make sense to me - How do you go from +7 to -7 back to +?

Do you agree that the expression is equal to \(\displaystyle -4\sqrt{3}-7\)? This comes about because you are dividing the numerator by -1.

 

[hemmed]

Do you agree that the expression is equal to \(\displaystyle -4\sqrt{3}-7\)? This comes about because you are dividing the numerator by -1.

Yes, i had a complete brain fail and didn't realise that \(\displaystyle -[4\sqrt{3}+7]\) is obviously the same flipping thing as \(\displaystyle -4\sqrt{3}-7\).

Time to revise those negative numbers