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A positive integer is 10 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is frac(2,3), then find the two integers.

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Okpalawalter8idn

The two integers are are mathematically given as

x=3.70

y=13.7

What is  the two integers?

Generally, the equation for the two integers is mathematically given as

x + 10 = y

1/x + 2/y = 2/3

Substitute

1/x + 2/x+10 = 2/3

Multiply by 3

3/x + 6/x + 10 = 2

Multiply by x

2 + 6x/x + 10 = 2x

Multiply by x + 3

2(x + 10) + 6x = 2x(x + 3)

2x+20+6x=2x^2+6x

-2x^2+2x+20=0

x=3.70

hence y

x + 10 = y

3.70+ 10 = y

y=13.7

In conclusion,  the two integers are

x=3.70

y=13.7

Read more about integers

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