1.) x2+y2=45,xy=18,then 1/x+1/y=? 2.)when a square is constructed on 3 sides of a triangle ,their sides are in the ratio 1:3:4,THE WAT triangle is it?  two questions are in caterpillar company?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll solve just the 1st problem since you have to ask only one question.

To determine the sum of the fractions we'll have to determine the least comon denominator, which is xy.

1/x + 1/y = (y+x)/xy

We already know the value of xy, which is 18. We'll calculate the value of x + y.

For this reason, we'll have to create a perfect square to the left side:

(x^2 + y^2 + 2xy) - 2xy = 45

(x+y)^2 = 45 + 2xy

x + y =`+-` `sqrt(45+2*18)`

x + y =`+-` `sqrt(81)`

x+  y = `+-` 9

Now, we'll calculate the requested sum:

1/x + 1/y = (y+x)/xy

Let x+y=9 => (y+x)/xy = 9/18 = 1/2

Let x+y=-9 => (y+x)/xy = -9/18 = -1/2

The requested values of the sum 1/x + 1/y are {-1/2 ; 1/2}.

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