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Math Problem
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# Math Problems and Solutions (Math Problem Sample)

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1. If x2 + 4y2 = 40 and xy = 6, what will be the value of x + 2y?
all the procedures used in the computation must be clearly shown with thier relevant formulas. nbo reference is reguired for the computatiuon. use apa formating style and adhere to the time provide. any cpoied work or answer without clear procedure will not be accepted.

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Mathematics
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1. If x2 + 4y2 = 40 and xy = 6, what will be the value of x + 2y?
We start by forming two equations;
xy = 6………………………equation 1
x2 + 4y2 = 40
bring 40 to the left side of the equation
thus we have
x2 + 4y2 - 40= 0………...equation 2
make x the subject of the formula in equation 1
thus we have
x = 6/y…………………….equation 3
substitute the value of x in equation 2
(6/y)2 + 4y2 = 40
36/y2 + 4y2 =40
bring 40 to the left side of the equation
36/y2 + 4y2 - 40 = 0
Multiply through by y2
36 + 4y4 – 40y = 0
Rewrite in the form ax4 +bx2 + c= 0
4y4 – 40y + 36 = 0
Divide through by 4
y4 – 10y + 9 = 0…………..equation 4
now we substitute y2 with p in equation 4
so
p2 – 10p + 9 = 0……………………equation 5
factorizing -10p, we get –p and -9p which can be added to get -10p
thus
p2 – p – 9p + 9 = 0
p(p-1) – 9(p-1)= 0
(p-9)(p-1)= 0
Thus
p-9

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