Math Olympiad | Square Root Simplification | only one solution satisfied

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[@thelifeclass]

Interesting 🎉

[@gokulc9375]

2+√x=√2
√x=2-√2
Square on both sides
x=(2-√2)^2
(a-b)^2=a^2+b^2-2ab
So,x=(2)^2+(√2)^2-2(2)(√2)
x=4+2-4√2
x=6-4√2
Very simple

[@paperino696969]

questa è la soluzione, non quel manicomio che sta sviluppando

[@RyanLewis-Johnson-wq6xs]

Sqrt[2]+Sqrt[x]=2 x=6-4Sqrt[2]

[@Andy-sg7bg]

The 1st step isolate variable term.

[@RyanLewis-Johnson-wq6xs]

It’s in my head.

[@papaayah]

How abaut :
Sqrt 2 + sqrt x = 2
Sqrt x = 2 - sqrt 2
(Sqrt x)^2 = (2 - sqrt 2)^2
× = 2^2 - 2.2.sqrt 2 + (sqrt 2)^2
X = 4 - 4sqrt 2 + 2
X = 6 - 4 sqrt 2
This more simple

[@АндрейПергаев-з4н]

Странный метод решения
Sqrt x=2-sqrt 2
Все возвести в квадрат и всё, 15 секунд на решение
х=6-4sqrt2

[@ferbre3520]

i got it right

[@TWJRPGGamming]

6-4*(2)^(1/2)

[@pascallemesle]

why do you complicate each step of your solution? I solve it in 3 lines.

[@hamdikurdi1277]

all your providing equations too complicated not easy to solve. thank you

[@5Xum]

Way over complicating. Move sqrt2 to right side at step 1 and get sqrtx = 2-sqrt2. Square both sides and you get
x=(2-sqrt2) ^2=4-4sqrt2+2=6-sqrt2, end of story

[@andreaskronemann9912]

That was exactly what I thought 😂

[@nandisaand5287]

Holy over-complications, Batman!
Just Isolate X, THEN do algebra:
SQRT(2) + SQRT(X) = 2
-SQRT(2) -SQRT(2)
SQRT(X) = 2 - SQRT(2)
{Square both sides...}
X = (2-SQRT(2))²
= 4 - 4•SQRT(2) +2
X=6 - 4•SQRT(2)
Simple. No quadratic eqns, no +/- foolishness, no SQRT(SQRT(...)) ridiculousness

[@CharlesChen-el4ot]

X = (2 + 2^1/2)^2
=4+2+4*2^1/2
=6+ 4*2^1/2

[@xanderbauer]

You have it too complicated