If x^2 + y^2 = 70 and 8xy = 40

what is the value of (x + y)^2

If x^2 + y^2 = 70 and 8xy = 40

what is the value of (x + y)^2

Tutors, please sign in to answer this question.

Go straight forward:

(x + y)^2

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

= 70 + 10, since 8xy = 40, 2xy = 10

= 80

8xy=40, xy=5, y=5/x

x^2 + (5/x)^2 = 70, x^4 -70x^2 +25 = 0

(x^2)^2 -70x^2 +25 =0, use quadratic formula to solve for x^2

x^2=35±20(3)^(1/2), x = ±(35±20(3)^(1/2))^(1/2)

Just using the positive values of the (±) signs,

=((35+20(3)^(1/2))^(1/2) + 5/(35+20(3)^(1/2))^(1/2))^2

=35 + 20(3)^(1/2) + 10 + 25/(35+20(3)^(1/2)

=35 + 20(3)^(1/2) + 10 + (25/(35+20(3)^(1/2))*((25/(35-20(3)^(1/2)/(25/(35-20(3)^(1/2))

=35 + 20(3)^(1/2) + 10 +35 - 20(3)^(1/2)

=80

The remaining 3 solutions are left.

there are a few approaches you could take here but... from the looks of it the easiest is to recognize 2 things:

x^{2} + y^{2} = 70

xy = 40/8 = 5

Now multiply out the third equation and substitute the values in:

(x+y)^{2} = x^{2} + 2xy + y^{2}

regrouping should make this easy to see from the first 2 equations above, I'll leave the final answer to you:

(x^{2} + y^{2}) + 2*(xy) = ???

Nikunj P.

Math and Science Specialist, Over 14 Years of Educational Experience

Scarsdale, NY

4.9
(88 ratings)

Anna L.

Affordable Columbia Educated Engineer

New York, NY

4.7
(7 ratings)

Steven M.

Premium Test Prep and Subject Tutor - New York City UWS

New York, NY

5.0
(179 ratings)

## Comments

80 !!

Thank you.