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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.

Sagot :

okpalawalter8

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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