Math Olympiad Algebra Problem | Square Root Simplification | Find X

[@lajosbogos8260]

49

[@IsraSirampa]

x^½ + (x-40)^½ = 10
(x-40)^½ =10 - x^½
(x-40)^½)^² = (10 - x^½)^²
x - 40 = 10^² - 20(x^½)+(x^½)^²
x- 40=10^² - 20(x^½)+x
- 40 = 10^² -20(x^½) + x-x
-40 =10^² - 20(x^½)
20(x^½) =10^² +40
20(x^½) =100 + 40
20(x^½) = 140
x^½ = 140/20
x^½ = 7
(x^½)^² = (7)^²
x = 7^²
x = 49
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X = 49;
(x^½)+(x-40)^½ = 10
49^½ + (49 - 40)^½ = 10
(7^²)^½ + 9^½ = 10
7^¹ + (3^²)^½ = 10
7^¹ + 3^¹ =10
10 = 10
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[@lajosbogos8260]

49