It would be easier to just square both sides from the original equation. (sqrt(a)+sqrt(-a))^2=144 a + 2sqrt(-a^2) - a = 144 2sqrt(-a^2) = 144 sqrt(-a^2) = 72 -a^2 = 72^2 a^2 = -72^2 a = +/- sqrt(-72^2) a = +/- 72i
7 minutes for that is insane! √a+√(-a)=12 √a+√(-a) = √a (1+√(-1))=√a (1+(e^iπ)^0.5 )=√a(1+e^(iπ/2)) =12 square the two terms a(1+e^(iπ/2) )^2=a(1+2e^(iπ/2)+e^iπ )=a(1+2ae^(iπ/2)-1)=2ae^(iπ/2)=144 a=144/(2e^(iπ/2) )=72e^(-iπ/2)=-72i ±a=72i
I don't think the last step is correct. (I) Shouldn't be there. You can't sperate (-72)² as (72²)(-1), it's probably (72)²(-1)². Which would make all the numbers positive. And if we take root of such numbers there is no + or -. It's only +. I think it's called taking a "modulus"
in the third line, instead of squaring both sides, you should simplify the term on the right by multiplying it by the conjugate, then it becomes: sqrt(a) = 12/(1+i) * ((1-i)/(1-i)) sqrt(a) = 12(1-i)/(1+1) sqrt(a) = 6(1-i) a=(6(1-i))² = 36 -72i -36 = -72i
Wowww How Have you done that ? You're genius
@@Zozo3-y2c Thanks 😔
Great bro
It would be easier to just square both sides from the original equation.
(sqrt(a)+sqrt(-a))^2=144
a + 2sqrt(-a^2) - a = 144
2sqrt(-a^2) = 144
sqrt(-a^2) = 72
-a^2 = 72^2
a^2 = -72^2
a = +/- sqrt(-72^2)
a = +/- 72i
7 minutes for that is insane!
√a+√(-a)=12
√a+√(-a) = √a (1+√(-1))=√a (1+(e^iπ)^0.5 )=√a(1+e^(iπ/2)) =12
square the two terms
a(1+e^(iπ/2) )^2=a(1+2e^(iπ/2)+e^iπ )=a(1+2ae^(iπ/2)-1)=2ae^(iπ/2)=144
a=144/(2e^(iπ/2) )=72e^(-iπ/2)=-72i
±a=72i
he loves his handwrighting
(6)+( ➖ 6) (3^3)+( ➖ 3^3) (1^1)+( ➖ 3^1) ( ➖ 3^1) (a ➖ 3a+1).
I don't think the last step is correct. (I) Shouldn't be there. You can't sperate (-72)² as (72²)(-1), it's probably (72)²(-1)². Which would make all the numbers positive. And if we take root of such numbers there is no + or -. It's only +. I think it's called taking a "modulus"
Checking the guy's answer with wolfram alpha, he is indeed correct.
actually it is not (-72)² but rather -72² and then you can separate
@@mateusbarbosakopp1387 so I would have been correct if it was -72² but since thier are brackets (-72)² i am wrong? Interesting property.
Can someone tell me whats wrong with:
sqrt(a) + sqrt(-a) = 12
sqrt(a)(1 + i) = 12
sqrt(a) = 12/(1 + i)
a = (12/[1 + i])^2
a = 144/(1 + i)^2
a = 144/2i
a = 72/i
in the third line, instead of squaring both sides, you should simplify the term on the right by multiplying it by the conjugate, then it becomes:
sqrt(a) = 12/(1+i) * ((1-i)/(1-i))
sqrt(a) = 12(1-i)/(1+1)
sqrt(a) = 6(1-i)
a=(6(1-i))² = 36 -72i -36 = -72i
@mateusbarbosakopp1387 thanks so much. How come you have to multiply by the conjugate first though? Is it simply because i is in the fraction?
72/i = (72/i)*(i/i) = 72i/(-1) = -72i
There's nothing wrong in 72/i
@@rickie_coll ah that makes sense. since i is its own thing i forgot that its really the same as having a radical in the denominator lol