Mymathware Shafii's math academy

From UDUS to KMUTT: The journey of a thousand miles ends with a PhD in Mathematics by Abubakar Muhammad Shafii Dr. Ibrahim Hassan Abdulkareem An anonymous sp…

Evaluate $x$ in the equation $\frac{x^2-10}{x-3}+\frac{1}{x-3}=\frac{1}{5}$ Solution First we need to find the Lowest Common Multiple (LCM) of the left hand …

Echoes of Victory from KMUTT - An epistle of accolades on Dr. Jamilu Abubakar Academia is a field of patience and resilience, only those who are willing to …

Let $f:A\rightarrow{A}$ with $f(x)=\frac{x+2}{x-3}$ for $A=\mathbb{R}/\{1,3\}$ Show that $f$ is a one-to-one function. Proof: we are given $f:A\rightarrow{A}…

Let $a,b\in\mathbb{R}$. Prove th inequality $\frac{a}{b}+\frac{b}{a}\geq{2}$ Proof We are given $\frac{a}{b}+\frac{b}{a}\geq{2}$, . Let $(a-b)^2\geq{0}$ so t…

a) We are to find area of $\bigtriangleup{ABC}$ This is quite simple, all we need to do is to use the idea of similar triangles, to do this, simply extract the $\bigtria…

Proof that for any integer $n>1$ the number $n^5+n^4+1$ is not a prime. Simply rewrite $n^5+n^4+1$ as $n^5+n^4+n^3-n^3-n^2-n+n^2+n+1$ Factor out common terms  $n^3(n^…

The product of the third and the sixth terms of an arithmetic sequence is $406$. The ninth term of the sequence divided by the fourth term gives a quotient of $2$ and a …

Find the sum of all natural numbers between $1$ and $1000$ that are not divisible by $13$. Let $S$ be the unknown sum and $M$ multiples of $13$ less than $1000$, then $S…

Lecture series by Dr Kamran Khan on Complex Integration Kamran Khan is an assistant professor at the department of mathematics, Aligarh Muslim Universi…

Solve the equation $2\cosh{2x}+10\sinh{2x}=5$ ................. 🆔 This is a hyperbolic trigonometric function equation, in order to solve the given equation, we must re…

Find the integer solution $x^2+3x+9=9y^2$.............(1) This is a beautiful quadratic Diophantine's equation that requires an integer solution. So how …

Find the value of $x$ $\frac{x^{\sqrt{x}}} {\sqrt{x}}=\frac{{\sqrt{x}}^x}{\sqrt{x}}$ Since both sides of the equation have a common denominator, multiply through by $\sq…