The Biotic World

Why x to the power zero is equals to one not zero: x^0 = 1 ?

Power in mathematics means number of times it multiplied with itself. Its represented by x a , where x is the number and a i…

byAmlesh Mahato •November 20, 2022

What is logarithm ? - Types Of Log - 10 Basic Laws Of Log

Here we discuss about What is log and its properties ? What are the 3 fundamental properties of logarithms?, What is the …

byAmlesh Mahato •August 19, 2022

What is Relations in sets - Definition, Types And Representation

Now suppose A and B be two subsets of the set of integers. Then some elements of A may be related  to some elem…

byAmlesh Mahato •April 04, 2022

Show that a^2+b^2>2ab

Solution : ⇨ We have to prove           ⇨ We Know            Proved

byAmlesh Mahato •July 02, 2021

Show that \left ( a+b+c \right )\left ( \frac{1}{a}+ \frac{1}{b}+\frac{1}{c} \right )\geq 9

Solution: ⇨ We have to show that           ⇨If a, b, c>0 then Arithmetic Mean  ⇨If a, b, c>0 then Geometric Mean  ⇨Now…

byAmlesh Mahato •June 29, 2021

Show that \left ( a+b \right )\left ( \frac{1}{a}+ \frac{1}{b} \right )>4

Solution: ⇨ We have to show           ⇨ Adding 2ab On both side  Proved

byAmlesh Mahato •June 29, 2021

If a > 0, b > 0, a > b then \frac{1}{a}<\frac{1}{b}

Solution: ⇨ We have e to show           ⇨Given that ⇨ ⇨ ⇨Again   Proved

byAmlesh Mahato •June 29, 2021

Show that \large a+\frac{1}{a}>2 or \frac{a+1}{a}>2

Solution:    Or    ⇨ Given       Proved

byAmlesh Mahato •June 29, 2021