A Very Nice Math Olympiad Problem | Solve for all values of x | Algebra

[@1234larry1]

Very good!

[@GeoVars]

10

[@key_board_x]

@ 6:27 / 12:21
(x - 3)² + 7² = 0
(x - 3)² = - 7²
(x - 3)² = 7²i²
x - 3 = ± 7i
x = 3 ± 7i

[@stevesilverman3505]

I was just going to take the 4th root of both sides and x-3=+7 and -7, and x=10 and -4. but that leaves out the two complex answers.

[@에스피-z2g]

x-3=7, x=10
x-3=-7, x=-4
x-3=7i, x=3+7i
x-3=-7i, x=3-7i

[@alucardthespy5539]

(x - 3)^4 = 7^4
Sqrt both sides
(x - 3)^2 = ±(7^2)
Positive 7^2
(x - 3)^2 = 7^2
Sqrt both sides
x - 3 = ±7
Add 3 to both sides
x = 3 ± 7 = 10 ; -4
Negative 7^2
(x - 3)^2 = -(7^2)
Sqrt both sides
x - 3 = ±7i
Add 3 to both sides
x = 3 ± 7i = 3 + 7i ; 3 - 7i
x = 3 - 7i; 3 + 7i; -4; 10

[@hangthuy458]

X-3=7
X=7+3=10

[@kidas0808]

(x-3)**4=7**4; ((x-3)**4)**(1/4)=((7**4)**(1/4); (x-3)=7; x=7+3=10, x=10

[@rauligvg]

Cool but I don’t think this is a math Olympics question

[@Luffi98]

I was thinking that it was absurdly obvious and it was just 10 and -4 without any fancy stuff. Then I saw imaginary numbers 💀

[@kajalbanerjee8220]

10