Ok. Thank you verrry much! I understand it now.
Is every thing here difficult? Because I'd like to stay here for a moment and discover more.
But if every thing is very very difficult, I can't understand it.
Not quite!
$\displaystyle (x-y)^2=9^2=81$
You must multiply out (x-y)(x-y)
When you do that, part of it is $\displaystyle x^2+y^2$
and the other part is -2xy.
You are given xy=12
therefore there is enough information to figure out $\displaystyle x^2+y^2$
from those clues, which gives the combined area of the 2 rooms.
Exactly,
it's a matter of learning the foundations and building up your skills from there.
When you don't understand something, there may be something which precedes it
that you need to go back and master first.
Something is "easy" to the extent that you know the component parts,
the "building blocks", the earlier material that should have been covered.
Ok, I'll try to explain some other way to solve the problem...
You got the equations?
xy = 12
y - x = 9
From the second equation, you know that we can put it in this form: y = 9 + x ?
From this, you 'know' what is y. Replace This, by the red 'y' in the first equation, like this:
x(9 + x) = 12
This done, you can expand, to give:
$\displaystyle 9x + x^2 = 12$
Then, you put everything on the same side, changing the order to make it easier, like this:
$\displaystyle x^2 + 9x - 12 = 0$
Now, you'll need to factorise. However, using the ordinary methods, it is impossible to solve this unless you know how to use the quadratic formula. So, we'll change some things a little.
We are looking for the sum of the rooms' areas. This means, we need to add $\displaystyle x^2$ and $\displaystyle y^2$
We're looking for $\displaystyle x^2 + y^2$
But we know that
y - x = 9
So... why not square everything to see what happens?
$\displaystyle (y-x)^2 = 9^2$
From your knowledge of expansion, you know that: $\displaystyle (y-x)^2 = (y-x)(y-x) = x^2 - xy - xy + y^2 = x^2 + y^2 - 2xy$
and $\displaystyle 9^2 = 81$
Hm... we have only part of our solution... there is this '-2xy' which we don't have! But... do you remember the first equation (the one I underlined)?
xy = 12
What we need is -2xy... so, let's multiply by -2.
xy (-2) = 12 (-2)
-2xy = -24
Now! We got -2xy. Let's replace this in the equation above, that is: $\displaystyle x^2 + y^2 - 2xy = 81$
$\displaystyle x^2 + y^2 (- 2xy) = 81$
$\displaystyle x^2 + y^2 (-24) = 81$
$\displaystyle x^2 + y^2 -24 = 81$
$\displaystyle x^2 + y^2 = 105$
Let me know if it's better, or if not, where you get stuck
Dear Wissem,
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What is this? something good or bad?
It's actually... bad. Your question needed a more appropriate title. Try not repeating the same mistake again.
I know it's difficult since you're more used to Dutch... but if you are in this forum, you'll have to learn to be more at ease with English...
Hm... I don't know how you learned it, that's the problem...
The way I learned it, is:
Multiply x in the first bracket by the first x in the second bracket. This gives $\displaystyle x^2$
Then, multiply x in the first bracket by -y in the second bracket. This gives $\displaystyle -xy$
Then, multiply -y in the first bracket by x in the second bracket. This gives $\displaystyle -xy$
Finally, multiply -y in the first bracket by -y in the second bracket. This gives $\displaystyle +y^2$
If you learned it like in Archie Meade's posts, then you might better understand it the other way.
Hmm... okay, multiplying x by x, gives $\displaystyle x^2$
Like:
$\displaystyle x \times x = x^2$
$\displaystyle 2 \times 2 = 2^2$
$\displaystyle y^2 \times y^2 = (y^2)^2$
Do you understand how the power works? Usually, what you need to remember for these is that when you get two things similar being multiplied, you put a little 2 at the upper right side of a number or symbol.
If you had:
$\displaystyle a \times a \times a = a^3$
$\displaystyle x \times x \times x \times x = x^4$
Is that good?
Or I did not understand what you did not understand?