No Calculator System of Equations

Algebra Level 2

Let x 2 + y 2 = 36 { x }^{ 2 }+{ y }^{ 2 }=36 and x y = 32 xy=32 . What is the positive value of x + y x+y ?


The answer is 10.

Andy Wong by Andy Wong , 22, USA

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

\(\begin{array}{} (x + y)^{2} &= x^{2} + 2xy + y^{2} \\ &= (x^{2} + y^{2}) + 2(xy) \\ &= 36 + 2(32) \\ &= 100 \\ (x + y) &= \sqrt{100} \\ &= 10 \end{array}\)

7 Helpful 0 Interesting 0 Brilliant 0 Confused

Yeah that's probably the best way to do it

Andy Wong - 5 years, 8 months ago

Log in to reply

Well I don't know any other solution except that. Are there any other way?

John Michael Gogola - 5 years, 8 months ago

Log in to reply

Isolating x or y and substituting it into the other equation takes much longer but works as well.

Andy Wong - 5 years, 8 months ago

Log in to reply

@Andy Wong – Ah substitution maybe,but that's so long task.

John Michael Gogola - 5 years, 8 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...