Indian Olympiad Mathematics | High school students.

This is beautifully solved. Rate the teaching skills #olympiad #equation #exponential #algebra #maths #mathstricks

[@aldoaldoz]

May be an esasier solution is the following.
√2 + √x = 2
means
±√2 ±√x = 2
±√x = 2 ±√2
Since 2 - √2 > 0, we can semplify the above to
+√x = 2 ±√2
Solution 1:
(√x)² = (2 +√2)²
x₁ = 6 + 4√2
[ check: -√2 +√(6 + 4√2) = 2 ]
Solution 2:
(√x)² = (2 -√2)²
x₂ = 6 - 4√2
[ check: +√2 +√(6 - 4√2) = 2 ]

[@BobbyMbock]

From the begining sqrtx=2+sqrt2 and then raise them all to the power of 2. And we are done.

[@hassanmorocco9968]

Merci

[@PhilCoolMath]

❤

[@ericmariaud8237]

Faux, il n'y a qu'une solution.
(√2 + √x)² = 2²
2 + 2√(2x) + x = 4
2√(2x) = 2 - x x > 0 et 2 - x > 0
0 < x < 2
6 + 4√2 > 2 n'est pas une solution
Plus simplement:
√2 + √x = 2 √x = 2 - √2 x = (2 - √2)² x = 6 - 4√2

[@БелАлекс]

Ой, а зачем же так все сложно? sqrt(x)= 2-sqrt(2). Ну и так де как вы возводил в квадрат. Самое главное знак +/- перед корнем не потерять.

[@christiann1058]

La tâche aurait été plus simple si 2 passait de l'autre côté de l'égalité. De plus la solution négative ne peut être réponse dans lR

[@PhilCoolMath]

❤

[@thediplomat6165]

3.5

[@PhilCoolMath]

Thanks ❤

[@ΜΙΧΑΗΛΘΕΟΔΩΡΟΠΟΥΛΟΣ-π1ξ]

is is fault
second solution > 10 not verified

[@christiann1058]

Je veux dire racine de 2

[@PhilCoolMath]

❤