If ${a^b} = 4 - ab$ and ${b^a} = 1$, where a and are b positive integers, find a.
$
{\text{A}}{\text{. 0}} \\
{\text{B}}{\text{. 1}} \\
{\text{C}}{\text{. 2}} \\
{\text{D}}{\text{. 3}} \\
$
Answer
385.8k+ views
Hint- A number of the form ${b^a}$ can be equal to one only if either b = 1 or a = 0.
In this question we have been given ${a^b} = 4 - ab$ and ${b^a} = 1$
And we know that ${b^a}$ can be equal to one only if either $b = 1$ or $a = 0$.
But we are given that $a$ and are $b$ positive integers
So, $a \ne 0$ $ \Rightarrow b = 1$
Now if we put $b = 1$ in the equation ${a^b} = 4 - ab$
We get,
${a^1} = 4 - a\left( 1 \right)$
$ \Rightarrow 2a = 4$
So, $a = 2$
Here the correct answer is option (C).
Note- In these types of questions, the most important part is the domain of our variables, most of us miss this point and get struck as they give two answers. So, all the given constraints should be taken into consideration while solving the question.
In this question we have been given ${a^b} = 4 - ab$ and ${b^a} = 1$
And we know that ${b^a}$ can be equal to one only if either $b = 1$ or $a = 0$.
But we are given that $a$ and are $b$ positive integers
So, $a \ne 0$ $ \Rightarrow b = 1$
Now if we put $b = 1$ in the equation ${a^b} = 4 - ab$
We get,
${a^1} = 4 - a\left( 1 \right)$
$ \Rightarrow 2a = 4$
So, $a = 2$
Here the correct answer is option (C).
Note- In these types of questions, the most important part is the domain of our variables, most of us miss this point and get struck as they give two answers. So, all the given constraints should be taken into consideration while solving the question.
Recently Updated Pages
Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts
Which one of the following places is unlikely to be class 8 physics CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is 1 divided by 0 class 8 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

Difference Between Plant Cell and Animal Cell

Find the HCF and LCM of 6 72 and 120 using the prime class 6 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers
