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Help with maths question

The full question is

The difference of two numbers x and y is 8 where x is greater than y
Find the minimum value of 4x(squared) - 3y(squared)

Would reallllly appreciate any help, thanks!
Original post by danielman98
The full question is

The difference of two numbers x and y is 8 where x is greater than y
Find the minimum value of 4x(squared) - 3y(squared)

Would reallllly appreciate any help, thanks!


So we know that xy=8x-y = 8 hence x=8+yx=8+y.

We wish to minimise z=4x2+3y2z=4x^2+3y^2 which can be rewritten as z=4(8+y)2+3y2z=4(8+y)^2+3y^2.

Min value can be found by completing the square.
Reply 2
Original post by RDKGames
So we know that xy=8x-y = 8 hence x=8+yx=8+y.

We wish to minimise z=4x2+3y2z=4x^2+3y^2 which can be rewritten as z=4(8+y)2+3y2z=4(8+y)^2+3y^2.

Min value can be found by completing the square.

Could you not differentiate z=4x2+3y2z=4x^2+3y^2, set equal to 0, substitute x=8+yx=8+y, find the value of y, find the value of x, and resubstitute back into your equation for z?
(edited 5 years ago)
Original post by Clarkest
Could you not differentiate z=4x2+3y2z=4x^2+3y^2, set equal to 0, substitute x=8+yx=8+y, find the value of y, find the value of x, and resubstitute back into your equation for z?


Yes this is a valid approach, but this thread was originally in GCSE forum so I didn’t suggest this approach for that level.
Reply 4
Original post by RDKGames
Yes this is a valid approach, but this thread was originally in GCSE forum so I didn’t suggest this approach for that level.

Oh, apologies... is completing the square a GCSE method now? I only got taught it at A Level :redface:
Original post by Clarkest
Oh, apologies... is completing the square a GCSE method now? I only got taught it at A Level :redface:


Yeah it was always at GCSE. Strange you never encountered it.
Reply 6
Original post by RDKGames
Yeah it was always at GCSE. Strange you never encountered it.

differenciation is actually the correct approach for our course according to our textbook, im in northern ireland so course might be a bit diffirent
Reply 7
Original post by RDKGames
Yeah it was always at GCSE. Strange you never encountered it.

I might be misremembering it... I know I definitely had to know it for my FSMQ course, which was the year after my GCSE.
Original post by danielman98
differenciation is actually the correct approach for our course according to our textbook, im in northern ireland so course might be a bit diffirent


Alright, are you comfortable using differentiation to solve this question then?
Reply 9
Original post by RDKGames
Alright, are you comfortable using differentiation to solve this question then?

yeah i am, its a new topic to me we only started it yesteday and im pretty lost in it to be honest haha

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