Identities level: normal

Algebra Level 2

If x + y = 5 x + y= 5 and x y = 3 x y = 3 , what is the value of x 2 + y 2 ? x^2+y^2?


The answer is 19.

Ömer Ertürk by Ömer Ertürk , 15, Turkey

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1 solution

James Watson
Jan 1, 2021

x + y = 5 ⟹ ( x + y ) 2 = x 2 + 2 x y + y 2 = 25 ⟹ x 2 + y 2 = 25 − 2 x y = 25 − 2 ( 3 ) = 19 \begin{aligned} x+y &= 5 \\ \implies (x+y)^2 &= x^2 + 2xy + y^2 = 25 \\ \implies x^2 + y^2 &= 25-2\blue{xy} = 25-2\blue{(3)} = \boxed{19} \end{aligned}

3 Helpful 3 Interesting 4 Brilliant 0 Confused

Wow, nice approach!

Kevin Klug - 5 months ago

Ooooh! Amazing!

Shane Sarosh - 2 months ago

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