Question
Session 2022) If the ratio between the fourth term from the beginning to the
fourth term from the end in the expansion of
equals
, then
fourth term from the end in the expansion of
, then
Ask by Phillips Warren. in Egypt
Dec 24,2024
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To solve the problem, we start by using the binomial expansion of the expression
.
The general term
in the expansion is represented as:
which simplifies to:
Now, the fourth term from the beginning (when
) is:
And the fourth term from the end (when
) is:
The ratio of the fourth term from the beginning to the fourth term from the end is given by:
We know from the problem’s condition that:
Setting these equal gives:
From the equivalence of the exponents of
and
, we derive two equations:
Solving the first equation:
And from the second equation:
Since both equations suggest
must be consistent, we find that:
The correct
that satisfies both the original equation and integer properties is
.
Thus, the answer is:
(b) 4