☺ Please answer with proper solution
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Bunti360:
Hello HridayAG, Can you give me edit option, I unfortunately posted it !..
HridayAg, Delete my answer, I will post it asap, I am trying it on a paper !
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Given Equation is (a^2 - b^2)x^2 + (b^2 - c^2)x + (c^2 - a^2) = 0.
The equation is in the form of ax^2 + bx + c = 0
Where a = a^2 - b^2, b = b^2 - c^2, c = c^2 - a^2.
Given that the equation has equal roots.
b^2 - 4ac = 0
(b^2 - c^2)^2 - 4(a^2 - b^2)(c^2 - a^2) = 0
b^4 + c^4 - 2b^2c^2 - (4a^2c^2 - 4a^4 - 4b^c^2 + 4a^2b^2) = 0
b^4 + c^4 - 2b^2c^2 - 4a^2c^2 + 4a^4 + 4b^2c^2 - 4a^2b^2 = 0
b^4 + c^4 + 2b^2c^2 - 4a^2c^2 + 4a^4 - 4a^2b^2 = 0
((-2a)^2)^2 + (b^2)^2 + (c^2)^2 - 2(2a^2b^2) + 2b^2c^2 + 2(-2a^2c^2) = 0
(-2a^2 + b^2 + c^2)^2 = 0
-2a^2 + b^2 + c^2 = 0
2a^2 = b^2 + c^2.
Therefore the answer is the option (B) - b^2 + c^2 = 2a^2
Hope this helps!
The equation is in the form of ax^2 + bx + c = 0
Where a = a^2 - b^2, b = b^2 - c^2, c = c^2 - a^2.
Given that the equation has equal roots.
b^2 - 4ac = 0
(b^2 - c^2)^2 - 4(a^2 - b^2)(c^2 - a^2) = 0
b^4 + c^4 - 2b^2c^2 - (4a^2c^2 - 4a^4 - 4b^c^2 + 4a^2b^2) = 0
b^4 + c^4 - 2b^2c^2 - 4a^2c^2 + 4a^4 + 4b^2c^2 - 4a^2b^2 = 0
b^4 + c^4 + 2b^2c^2 - 4a^2c^2 + 4a^4 - 4a^2b^2 = 0
((-2a)^2)^2 + (b^2)^2 + (c^2)^2 - 2(2a^2b^2) + 2b^2c^2 + 2(-2a^2c^2) = 0
(-2a^2 + b^2 + c^2)^2 = 0
-2a^2 + b^2 + c^2 = 0
2a^2 = b^2 + c^2.
Therefore the answer is the option (B) - b^2 + c^2 = 2a^2
Hope this helps!
If i write it as (2a^2)^2. Then there will be a mismatch in the equation.
There were to choices infront you, but you choose 1 exactly, why? , Don't get me wrong, I am just trying to convey my doubt, :) Have a Great day :D !
Oh ok, I got it !.. Thanks, :D !
In the starting comment, i said i was little bit confused. That is because I wrote (2a^2)^2. The answer I got is out of maths portion. Thats why i took (-2a^2)^2. Anyways we will get 4a^4.
Yeah, Thanks for the explanation :D !, Have a great day :) !
Wish u the same and gud n8, gud luck bro..
Thank you !.. :D
good ans, i am just thinking if any short will work here?
Thanks Bro
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