Thx for your explanation, i'm a middle school student have you a playlist for me, i just discovered your channel, and even i don't understand English (Thx to Google translate😅) i understand your methods
X=1 is the only solution for X^3+4x-5=0 =(x-1)*(x^2+x+5) because there is no X-value, for which the quadratic term is zero. Thanks to the teacher , he is a proper math- magician.
WHERE IT IS TOLD THAT "a' IS EQUAL TO f(x)? TO TAKE THE VALUE OF FUNCTION TO BE 3 TO SOLVE 'x'. ON SOLVING YOU R TELLING 'a' IS EQUAL TO 1 WHILE THE QUESTION SAYS a=3 . CONFUSING?
Prime Newtons is a radically good math teacher! 🎉😊
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Thx for your explanation, i'm a middle school student have you a playlist for me, i just discovered your channel, and even i don't understand English (Thx to Google translate😅) i understand your methods
Very good explanation Sir. Thanks 👍
X=1 is the only solution for
X^3+4x-5=0 =(x-1)*(x^2+x+5) because there is no X-value, for which the quadratic term is zero.
Thanks to the teacher , he is a proper math- magician.
WHERE IT IS TOLD THAT "a' IS EQUAL TO f(x)? TO TAKE THE VALUE OF FUNCTION TO BE 3 TO SOLVE 'x'. ON SOLVING YOU R TELLING 'a' IS EQUAL TO 1 WHILE THE QUESTION SAYS a=3 . CONFUSING?
But how do you know x=1 is only real solution to x^3+4x=5? If not, then the inverse is not defined at a=3 so no derivative, correct?
Absolutely. f must be a one to one differentiate function.
because original f(x) is always increasing since it's square root, it's one to one, so only one real solution.
x^3 and 4x are monotonically increasing, so their sum must also monotonically increase, which means every solution is unique
The derivative of the inside is 3x^2+4 which is always > 0 in the reals. Which means, it is strictly increasing. So it is one-to-one
Exactly!
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