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What's wrong in this proof?

-20=-20, now, 16-36=25-45, we add a perfect square to both side, 16-36+81/4=25-45+81/4, now both r perfect squares, (4-9/2)^2=(5-9/2)^2, taking square root on both sides, 4-9/2=5-9/2, cancelling both 9/2 as they have same sign and same value, 4=5 i.e. 2*2=5

Note by Chetan Shinde
4 years ago

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root of (4-9/2)^2=(5-9/2)^2 is wrong.......

root of something is always taken in modulus.....we can't cancel 9/2 from both sides.....therefore after this step everything is wrong........

and in this way we can prove anything....if we don't take modulus.....

i hope i'm making it clear what i'm saying...

u took 4=5 ............[1]

multiplied them and put a -ve sign

squared both sides in eq.[1]
we get 16=25 ........[2]

now to get -20=-20 ................u subtracted 16-36=25-45 ..........[3]

u took average of 4 and 5 i.e. 9/2 and squared it
i.e. (9/2)^2 = 81/4 and added in equation 3

u made it a perfect sq. (4-9/2)^2=(5-9/2)^2

therefore we can't write 4-9/2=5-9/2,

and hence |4-9/2|= |5-9/2|

i.e. |-1/2|=|1/2|

which is always 1/2=1/2 and hence a UNIVERSAL TRUTH........... Riya Gupta · 4 years ago

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@Riya Gupta modulus right???fine then the modulus function returns positive value of a variable or an expression. For this reason, this function is also referred as absolute value function. In reference to modulus of an independent variable, the function results in a non-negative value of the variable, irrespective of whether independent variable is positive or negative. For the sake of understanding, we consider a non-negative number "2" equated to modulus of independent variable "x" like :


Then, the values of “x” satisfying this equation is :

⇒x=±2 hence what changes is sign.not the value. and same number on both rhs & lhs can be cancelled if both have the same sign...modulus is not the mistake..mistake is the sign.the expression give 4 possibilities +=+ or +=- or -=- or -=+ and The modulus of an expression “x-a” is interpreted to represent “distance” between “x” and “a” on the real number line. For example :


This means that the variable “x” is at a distance “5” from “2”. We see here that the values of “x” satisfying this equation is :






The “x = 7” is indeed at a distance “5” from “2” and “x=-3” is indeed at a distance “5” from “2”. Similarly, modulus |x|= 3 represents distance on either side of origin. .its just a mistake of sign. Chetan Shinde · 4 years ago

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2+2=5?how Zsheeza Zafar · 3 years, 6 months ago

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the flaw is in the step when u take the square root on both sides the reason hs been explained in the form of an example:- suppose we tell that (x-2)^2 =(x-9)^2 now if we wanna take square root on both sides we get :- |x-2| = |x-9| tht is x-2 = + or-(x-9)

i hope u undrstnd wht i meant to tell in the above steps Mishti Angel · 4 years ago

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alsdkjf v jsdhv jkdshvj (don't even get anything) disfdjakshfjkdsh (so confused) alsdfjklsdjfklsdjf (ahhhhh!!!!!!!) dlfkjkldjfk Jess J · 4 years ago

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@Jess J what are you saying........??.....which language is it......is it a code language...!!!!!?? Raja Metronetizen · 4 years ago

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@Raja Metronetizen he has given the meaning of his funny language in brackets....:D Riya Gupta · 4 years ago

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truth sam... truth The Destroyer · 4 years ago

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4-9/2=-1/2 and 5-9/2=1/2 so you write (-1/2)=1/2 Arbër Avdullahu · 4 years ago

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@Arbër Avdullahu x-5=y-5 so we write x=y so we can write 4-9/2=5-9/2, 4=5 Chetan Shinde · 4 years ago

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