Math Problems and Solutions (Math Problem Sample)

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