Nice algebra problem | Find the value of X !!

Nice algebra problem | Find the value of X !!
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[@segaranpillay7154]

why are people so concerned about music in the bagkground . This just spoils concentration

[@MathEducation100M]

Nice trick

[@yodaami]

Ans 1) +isquareroot2. Answer 2) - i squareroot2. Ans3) zero. But what is the 4th solution?

[@Nguyễn-j9q]

X=0

[@yodaami]

Surely there are 4 solutions?

[@foca8495]

✔(x² + x²) = x²
[✔{2(x²)}]² = (x²)²
2(x²) = x⁴
[2(x²)] ÷ x² = (x⁴) ÷ x²
2 = x²
✔2 = x

[@dardoburgos3179]

X= 0.

[@victorchoripapa2232]

Option (d)

[@lakshmikutty2255]

√(x²+x²) =x² √ x=√22x=x²

[@user-si3ih4zx4q]

Почему всегда так громоздко?
х^2=|х|^2
|х|^2-2^(1/2)×|х|=0
|х| (|х|-2^(2)1/2)=0
|х|=0 |х|=2^(1/2)
х=0 х=+2^(1/2)
х=-2^(1/2)
Замечание. 2^(1/2) это корень квадратный из 2.
Пример устный!

[@pas6295]

Xis Root 2 and 0.

[@exam_pro]

-√2 also

[@himadrikhanra7463]

X= + or - root 2 but not = 0

[@PS-mh8ts]

0 also satisfies the given equation
√(x²+x²)=x² -- (i)
When x=0, we get LHS=√(0²+0²)=√(0+0)=√0=0
RHS=x²=0²=0
Thus LHS=RHS, and x=0 is a solution to (i)

[@ItsPREPP98]

X² = √(x²+x²)
x⁴ = x² +x²
x⁴ - x² = x²
x²(x²-1) = x²
Case 1: x = 0
Case 2: x =\= 0
then x²-1=1
x²-2=0
(x-√2)(x+√2) = 0
x = √2 or -√2

[@Sergey_K_-]

Решил в уме

[@exam_pro]

??

[@Sergey_K_-]

​@@exam_pro это решается легко. Без бумаги и записей. Просто в голове. Не надо целый лист писать. Все решается устно

[@dave929]

Root 2 or 0.

[@kalesmaster2768]

Square root 2

[@dave929]

@@kalesmaster2768 zero could also be a valid answer.

[@kalesmaster2768]

@dave929 I know but root 2≠ square root 2

[@dave929]

@@kalesmaster2768 Left side: root 2 squared plus root 2 squared totals 4. Square root of 4 is 2. The right side has x^2, which would come to 2, as well.

[@kalesmaster2768]

@dave929 you missed the word "square" in your answer "root 2"