Food & Drink1 min ago
Any mathematicians out there?
24 Answers
Can anyone take me through the resoultion of the equation
24/x = 10-x
By observation there are two answers, 4 and 6, but the process eludes me.
24/x = 10-x
By observation there are two answers, 4 and 6, but the process eludes me.
Answers
Best Answer
No best answer has yet been selected by barryjbutler. Once a best answer has been selected, it will be shown here.
For more on marking an answer as the "Best Answer", please visit our FAQ.This is a quadratic equation which will have 2 roots(answers). First get rid of the x on the bottom by multiplying each term by x. this gives:
24=10x-x^2
Then bring all the terms to the left side of the equal sign so it looks more familiar(remembering that anything you move must change sign). This will give;
x^2-10x+24=0
Now factorise into 2 brackets (hope you get that bit?)
So (x-6)(x-4)=0
So either x-6=0 so x is6 or x-4=0 so x is 4
24=10x-x^2
Then bring all the terms to the left side of the equal sign so it looks more familiar(remembering that anything you move must change sign). This will give;
x^2-10x+24=0
Now factorise into 2 brackets (hope you get that bit?)
So (x-6)(x-4)=0
So either x-6=0 so x is6 or x-4=0 so x is 4
Follow these steps
a) lose the denominator by multiplying both sides by 'x'
b) Take everything on the right-hand side and subtract it from both sides
You will be left with a quadratic function of 'x' equal to 0
c) factorise that function of 'x' into the form (ax +- b)(cx +- d)
If two expressions multiplied together = zero, then one of them must be 0
so either (ax +- b) = 0
or (cx +- d) = 0
d) Solve each of those for the two possible answers.
If you cannot factorise the quadratic, then use the formula for solving quadratics:
x = (-b +- SQR(b^2 -4ac)) / 2a
(I hope I have remembered that correctly from over 40 years ago)
a) lose the denominator by multiplying both sides by 'x'
b) Take everything on the right-hand side and subtract it from both sides
You will be left with a quadratic function of 'x' equal to 0
c) factorise that function of 'x' into the form (ax +- b)(cx +- d)
If two expressions multiplied together = zero, then one of them must be 0
so either (ax +- b) = 0
or (cx +- d) = 0
d) Solve each of those for the two possible answers.
If you cannot factorise the quadratic, then use the formula for solving quadratics:
x = (-b +- SQR(b^2 -4ac)) / 2a
(I hope I have remembered that correctly from over 40 years ago)
Have you not got a number pad on your keyboard? If not try this. I don't know if it will work but it does for me:
Turn on num lock. On my small keyboard the letters M J K L U I O generate the numbers 1 - 6, 7 to 9 being on the top row. So hold down ALT and type KIL instead. let me know if it works or not.
Turn on num lock. On my small keyboard the letters M J K L U I O generate the numbers 1 - 6, 7 to 9 being on the top row. So hold down ALT and type KIL instead. let me know if it works or not.
The keyboard I am using at the moment has no number pad but has a num lock key on the top right. I used that plus the letters I gave to generate ².
This might be useful to some people who want to generate diacritics and other symbols:
http://www.irongeek.c...combos-and-chart.html
This might be useful to some people who want to generate diacritics and other symbols:
http://www.irongeek.c...combos-and-chart.html