An Algebra Problem by Matthew Christopher Pohadi

Algebra Level 1

x and y are real numbers which satisfy : x 2 + 2 y + 4 + x 2 + x − y + 5 = x 2 + x + 3 y + 2 + x 2 + 2 x + 3 \sqrt{x^2+2y+4} + \sqrt{x^2+x-y+5} = \sqrt{x^2+x+3y+2} + \sqrt{x^2+2x+3} Find the value of (x+y)


The answer is 2.

Matthew Christopher Pohadi by Matthew Christopher Poha… , 19

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1 solution

Let A = x 2 + 2 y + 4 A= x^2+2y+4 B = x 2 + x − y + 5 B= x^2+x-y+5 and C = x + y − 2 C= x+y-2 Substituting this into the equation we get A + B = A + C + B + C \sqrt{A} + \sqrt{B} = \sqrt{A+C} + \sqrt{B+C} Hence we know that C=0 x+y-2=0, x + y = 2 x+y=2

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