A wrong problem before

Algebra Level 4

{ x 2 + x x y = 2016 y 2 + y x y = 252 \large{\begin{cases} x^2 + x\sqrt{xy} = 2016 \\ y^2 + y\sqrt{xy} = 252 \end{cases} }

Let x x and y y be positive real numbers satisfying the above system of equations. Evaluate x 2 − y 2 x^2-y^2 .

Inspiration: This was a problem of Shivam Jadhav with a small change.


The answer is 1260.

Chew-Seong Cheong by Chew-Seong Cheong , 63, Malaysia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Rohit Ner
Sep 18, 2015

x x ( x + y ) y y ( x + y ) = 8 ⇒ x = 4 y y 2 + 2 y 2 = 252 y 2 = 84 x 2 − y 2 = 15 y 2 = 1260 \begin{aligned}\frac{x\sqrt{x}\left(\sqrt{x}+\sqrt{y}\right)}{y\sqrt{y}\left(\sqrt{x}+\sqrt{y}\right)}&=8\\\Rightarrow x&=4y\\{y}^2+2{y}^2&=252\\{y}^2&=84\\{x}^2-{y}^2&=15{y}^2\\&\huge\color{#3D99F6}{=\boxed{1260}}\end{aligned}

12 Helpful 0 Interesting 0 Brilliant 0 Confused

Thanks for the solution.

Chew-Seong Cheong - 5 years, 8 months ago

That was way easy.

Department 8 - 5 years, 8 months ago

Log in to reply

Yes, I didn't see that earlier.

Chew-Seong Cheong - 5 years, 8 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...